Differential Equations II

Dr Mark Jones (PhD Maths)

- January 25, 2014

1

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# Description

Hi Guys,

This is a Smart Worksheet on second order linear differential equations covering both homogeneous and non-homogeneous types and including problems with initial conditions.

There are also some useful de solver tools where you can type in your own problems and obtain the worked solutions so you can check any homework that you have.

There's a PDF file for those who want to work on the sheet independently and an email math que, where you can jot down a questions and append it to an email. If I get time, I will write up a YouTube video solution and send you the link.

All the best with the worksheet and if you have any feedback just give us a buzz.

Cheers,

Mark

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# Reviews

Helpfulness

Newest

Rating

Helpfulness

All Versions

All Versions

Latest Version

4.3

57 total

5 40

4 8

3 1

2 1

1 7

Sabri Meviş

It doesnt work! I can open the app but when i click on the equation it gives error unexpectedly..

A Google User

Coll Nice

User reviews

Dr Mark Jones (PhD Maths) February 8, 2015

Cheeze :D Dr Mark Jones (PhD Maths) May 2, 2014

Cheers :) Dr Mark Jones (PhD Maths) March 19, 2013

It DOES work on the vast majority of phones and tablets. Sorry it's not worked out on yours. Dr Mark Jones (PhD Maths) September 29, 2013

Hey man, no probs...glad its helpful. Cheers and thanks for the review, Mark Dr Mark Jones (PhD Maths) March 19, 2013

Thanks Coll - appreciated Dr Mark Jones (PhD Maths) May 1, 2013

Hey good man...glad its of help. All the best, Mark Dr Mark Jones (PhD Maths) March 19, 2013

Hi the de solver sometimes does this at the server end - just click back and repeat ( i mention this in a toast when u click on the user guide) Dr Mark Jones (PhD Maths) July 3, 2013

Man O Man...Cheers, Mark :) Dr Mark Jones (PhD Maths) March 19, 2013

Hey - good man :) Review deleted

# Additional information

Updated

January 25, 2014

Size

172k

Installs

10,000 - 50,000

Current Version

3.0

Requires Android

2.1 and up

Content Rating

Everyone

Permissions

Report

Flag as inappropriate Offered By

Dr Mark Jones (PhD Maths)

# Similar

## Differential equations

Generally, differential equations calculator provides detailed solution

Online differential equations calculator allows you to solve:

Including detailed solutions for:

[✔] First-order differential equations

[✔] Linear homogeneous and inhomogeneous first and second order equations

[✔] A equations with separable variables

Examples of solvable differential equations:

[✔] Simple first-order differential equations

[✔] Differential equations with separable variables

[✔] Inhomogeneous linear differential equation of first order

[✔] Bernoulli differential equation

[✔] Exact differential equations

[✔] Linear homogeneous second order differential equations with constant coefficients

[✔] Inhomogeneous linear second order differential equations with constant coefficients

[✔] Differential equations, allowing reduction of the order

[✔] Linear homogeneous and inhomogeneous differential equations of higher order with constant coefficients

[✔] Supported all math symbols and functions. For example: sin(x), cos(x), exp(x), tan(x), ctan(x) and other.

[✔] Suported complex variables (solve complex equations)

The Calculator contain some features:

[✔] Some examples

[✔] Сorrect input expression errors

Examples for solve:

y' = x + e^x - 1

y' = 2x/(x^2 - 7)^(1/3)

e^y*dy = (x + sin(2x))dx

y' = y*(x^2 + e^x)

y' - 2*x*y/(1+x^2) = 1 + x^2

y'' + 3*y' = 0

x*y'' - xy' + y = 0

y'' - 2y' = (x^2 + 1)*e^x

x*y'' - xy' + y = x^2 + 1

(x^2 - y^2)dx - 2xydy = 0

y'''' + y''' - 5y'' + y' - 6y = x*cos(x) + sin(x)

4y^3*y'' = y^4 - 1

## Differential Equations I

Hi Guys, This is a Smart Worksheet on First Order Differential Equations including separable, homogeneous, Integrating Factor and Bernoulli.

The worksheet also contains an array of tools so that you can type in first order d.e. problems of your own.

A pdf file is also downloadable for those who prefer to work on the worksheet independently.

Hope you enjoy it and any feedback is always appreciated.

Cheers, Mark

## Equation Step-by-Step Calc

The equations calculator online (equation solver) contains the section:

This calculator return only anwser, but return ✪ detail step by step solution ✪ for

[✔] A quadratic equations

[✔] A simplest trigonometric equations

[✔] A equation with a module (for example, |x + 1| + |x^2 – 7| = 20)

The Supported:

[✔] Supported all math symbols and functions. For example: sin(x), cos(x), exp(x), tan(x), ctan(x) and other.

[✔] Suported complex variables (solve complex equations)

Solve any equation types, such as:

[✔] linear equations

[✔] square (quatratic) and cubic equations

[✔] polynomial equations

[✔] trigonometric equations

[✔] exponential equations

[✔] logarithmic equations

[✔] equations with complex numbers

[✔] and other

The Calculator contain some features:

[✔] Numeric solutions for unsolvable equations (such as cos(x) = x^3 - x + 2)

[✔] Some examples

[✔] Сorrect input expression errors (for example, you enter x^2-x+1/x - 1=0 or e^-x^2=5)

## Coupled Differential Equations

Upcoming changes:

1) Add a 2nd order coupled differential equation solver

2) Export solution data to txt, or csv format.

---

This app uses the runge kutta 4 algorithm to solve to coupled differential equations of the first order. The results are plotted and can be pinch zoomed. The workflow is streamlined via a custom keyboard and toast messages that help the user towards plotting a solution quickly.

This app is intended for students of science and engineering to get a qualitative understanding of how a coupled 1st order differential system behaves. Future versions of this app will let the user export data, generalize to "N" differential equations and also solve equations of the second order.

## 1st Differential Solver Free

Scientific tool/solver to solve “Single Variable Non-Linear First Order Ordinary Differential Equations”. The app is very useful for engineers, scientists, economists to study the behaviour of a non-linear system encountered in practical problems. The app computes the value of dependent variable at a given value of independent variable (with given initial values of dependent and independent variable).The relationship between dependent and independent can be visualized using the “Plot” function. The results along with the “Plot” can be sent to any e-mail id by using “Send e-mail” option. The app has a very rich and is very user-friendly UI (user interface). The results can be sent to any e-mail id by using “Send e-mail” option in main menu.

Please read the Equation format specified in help before attempting to solve complex non-linear equations.

The free version of the app can be found at

https://play.google.com/store/apps/details?id=com.ashermobile.math.diffsolver

This App is ad supported.

★ Application areas: Some of the applications areas are:

Physics and sciences

Engineering

Finance and Economics

Industry

Research

★ Who should buy this app?

-Researchers

-Engineers

-Engineering students

-Science students

★ Why buy this app?

- Solves differential equation in quick time

- Reduces time in calculations.

- Reduces effort and time in research.

★ Tips and Notes:

- It is always recommended that the user’s uses as smaller difference in final and initial X as possible to get “Higher accuracy” and “Better Resolution in Plot”. This can be done using the step process as described below.

- For example to find value of Y at 10 with initial value of X as 0 and Y as 0 for dY/dX=Cos(X)*Sin(X). To get higher accurate results split the range of 10 into 2 “steps” (0 to 5 and 5 to 10). For first step, enter the function and initial value of X as 0 and Y as 0 and final value of X as 5. Click “Calculate” to find value of Y at X=5 as “0.45976788”. Now for second step, enter the function and initial value of X as 5 and Y as 0.45976788 and final value of X as 10. Click “Calculate” to find value of Y at X=5 as “0.14979482”.

- When the app returns a “NaN”, either the (i) Y value doesn’t exist at the final X or (ii) range is too large, try reducing the difference in initial and final X and use the step process described above (this is especially needed for functions with large curvature like tan and log).

- Based on capability and limitations of Android system the maximum difference in initial and final X for “Calculate” and “Plot” as fixed as “50” and “30” respectively. For Y at a range greater than 30, use the step process described above. (For larger ranger of 400 and 100 for calculation and plotting, Please try Paid App)

★ Have Suggestions or Issues?

Email ashermobilesolutions@gmail.com and you'll get a prompt response.

## 2nd Differential Solver Free

Scientific tool/solver to solve “Single Variable Non-Linear Second Order Ordinary Differential Equations”. The app is very useful for engineers, scientists, economists to study the behaviour of a non-linear system encountered in practical problems. The app computes the value of Y and dY/dX at any given value of X (with given initial values of X, Y and dY/dX). The relationship between X-Y and X-dY/dX can be visualized using the “Plot Y” and “Plot yDot” functions respectively. The results along with the “Plot” can be sent to any e-mail id by using “Send e-mail” option. The app has a very rich and is very user-friendly UI (user interface). The results can be sent to any e-mail id by using “Send e-mail” option in main menu.

Please read the Equation format specified in help before attempting to solve complex non-linear equations.

Please read the Equation format specified in help before attempting to solve complex non-linear equations.

The paid version of the app can be found at

https://play.google.com/store/apps/details?id=com.ashermobile.math.diffsolver2

This App is ad supported.

★ Application areas: Some of applications areas are:

•Physics and sciences

•Engineering

•Finance and Economics

•Industry

•Research

★ Who should buy this app?

-Researchers

-Engineers

-Engineering students

-Science students

★ Why buy this app?

- Solves differential equation in quick time

- Reduces time in calculations.

-Reduces effort and time in research.

★ Tips and Notes:

• It is always recommended that the user’s uses as smaller difference in final and initial X as possible to get “Higher accuracy” and “Better Resolution in Plot”. This can be done using the step process as described below.

• For example to find value of Y at 10 with initial value of X as 0, Y as 0 and yDot as 0 for d2Y/dX2 =Cos(X)*Sin(X). To get higher accurate results split the range of 10 into 2 “steps” (0 to 5 and 5 to 10). For first step, enter the equation and initial value of X as 0, Y as 0, yDot as 0 and final value of X as 5. Click “Calculate” to find value of Y and yDot at X=5 as “1.3180026397909919” and “0.45976788267781876” respectively. Now for second step, enter the equation and initial value of X as 5, initial value of Y as 1.3180026397909919, initial yDot as 0.45976788267781876 and final value of X as 10. Click “Calculate” to find value of Y and yDot at X=10 as “2.3858818461857414” and “0.1479794846781928”.

• When the app returns a “NaN”, either the (i) Y and dY/dX value doesn’t exist at the final X or (ii) range is too large, try reducing the difference in initial and final X and use the step process described above (this is especially needed for functions with large curvature like tan and log).

• Based on capability and limitations of Android system the maximum difference in initial and final X for “Calculate”, “Plot” and “Plot yDot” as fixed as “50”, “30” and “30” respectively. For Y and dY/dX at a range greater than 50, use the step process described above. (For larger ranger of 200 and 100 for calculation and plotting, Please try Paid App)

★ Have Suggestions or Issues?

Email ashermobilesolutions@gmail.com and you'll get a prompt response.

## Calculus

Quick Revision before your test.

From novice to expert in Calculus.

Now Includes Tools for Calculation.Calculate Definite Integral,Plot Function Graphs,LCM,GCD.

==Gets installed in memory card.So no issues of Storage problems.

==Explains concepts in details includes(Definition,Theorems,Formula,Some Examples,Multimedia Graphics helps to get concepts clear)

-->Functions:

--->Limits

--->Continuity

--->Differentiability

--->Differentiation

---->Application Of Derivatives

--->Indefinite Integrals

--->Definite Integral

---->Area Under Curves

--->Differential Equations

From novice to expert in Calculus.

Now Includes Tools for Calculation.Calculate Definite Integral,Plot Function Graphs,LCM,GCD.

==Gets installed in memory card.So no issues of Storage problems.

==Explains concepts in details includes(Definition,Theorems,Formula,Some Examples,Multimedia Graphics helps to get concepts clear)

-->Functions:

--->Limits

--->Continuity

--->Differentiability

--->Differentiation

---->Application Of Derivatives

--->Indefinite Integrals

--->Definite Integral

---->Area Under Curves

--->Differential Equations

## Integral calculator

Full version. This app is 100%Free!

Users college level with some knowledge in integral and/or Fourier series will appreciate in depth all features of this app.

Integrals calculator is a powerful app to calculate indefinite and definite integrals and make a complete functions analysis of real variable.

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This app help in one variable real calculus, from Integrals, to Taylor polynomial. Also it calculates derivate, plot functions, Taylor Polynomial, derivate and so on ...

In resume, with Functions Integrator is able to do the following operations:

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## Mathematics

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Supported languages:

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Mathematics is a powerful calculation software for your android smartphone.

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## Math Solver

Solve Math problems and Plot functions.

Math Solver is a full featured scientific calculator and graphing calculator with widest range of functions available.

Solves problems in Basic Math, Algebra, Complex Numbers, Trigonometry, Integral and Differential Calculus, Set Theory, Matrix and vector Algebra

Math Solver is a full featured scientific calculator and graphing calculator with widest range of functions available.

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Support for trigonometric inverse-trigonometric and hyperbolic functions

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Note: Free version contains ads! In-app upgrade to PRO version to make it ad-free.

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Note- 1:- It doesn't solve word problems.

Note- 2:- It doesn't show steps to solve a problem. It solve shows final answer.

## Dynamical System Simulator

Dynamical System Simulator animates 2D and 3D first-order and second-order systems of differential equations in real time. Watch animated particles move through space leaving a trail in their wake. Great for verifying slope fields, phase portraits, and gaining an intuitive understanding of dynamical systems. Knowledge of differential equations is assumed but the help screen will point you to additional sources of information. The app is pre-loaded with several well known dynamical system configurations that can be selected from the navigation drawer. Parameters for a particular system type can be randomized.

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• x', y', z' (2nd Order Mode Only)

• t (time)

• sin (sine)

• cos (cosine)

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• acos (arccosine)

• abs (absolute value)

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• Logistic Population (1D)

• Periodic Harvesting (1D)

• Saddle (2D)

• Source (2D)

• Sink (2D)

• Center (2D)

• Spiral Source (2D)

• Spiral Sink (2D)

• Bifurcations (2D)

• Homoclinic Orbit (2D)

• Spiral Saddle (3D)

• Spiral Sink (3D)

• Lorenz (3D)

• Oscillations (3D)

Mode Settings:

• Matrix (linear) / Expressions (linear or non-linear)

• 2D / 3D

• 1st Order / 2nd Order

Simulation Settings:

• Number of Particles

• Update Rate

• Time Scale (including negative)

• Enable/Disable random initial velocities for particles

View Settings:

• Line Width

• Line Color

• Zooming (with pinch gestures)

• View Rotation (3D only)

In Expressions Mode the following symbols and trigonometric functions can be used:

• x, y, z

• x', y', z' (2nd Order Mode Only)

• t (time)

• sin (sine)

• cos (cosine)

• asin (arcsine)

• acos (arccosine)

• abs (absolute value)

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## Differential Calculator EQ2+IC

Hi Guys,

Enter a second order differential equation with initial conditions and this works out the solution, showing you it all step by step. It basically does just what it says on the tin. So if you have homework that you need to check out, then look no further.

The widget tool is taken from the selection of tools that appears on my live worksheet app entitled Differential Equations II, that appears on my developer page.

Hope it proves helpful.

Cheers,

Mark

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Issue Description:

Differential Equation, Application of Differential Equation, Exact Differential Equation (optional), Question Bank

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## yHomework - Math Solver

Having trouble with algebra?

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# More from developer

## Inequalities Calculator

Hi Guys,

Enter an inequality that is <, <=, >, >= or = and this works out the solution for you. It basically does just what it says on the tin. So if you have homework that you need to check the answers for, then look no further.

This tool is taken from the selection of tools that appears on my live worksheet app on Inequalities and the Modulus Function, that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

## Trig Identities Calculator

Hi Guys,

Enter any trig identity and this will calculate a selection of alternative forms. It does just what it says on the tin. So if you have work that you need to check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app entitled Trig Identities and Equations, that appears on my developer page.

Hope it proves helpful.

Cheers,

Mark

## Long Division Calculator

Hi Guys,

Enter two whole numbers and this does the long division, showing you it all step by step. It basically does just what it says on the tin. So if you have homework that you need to check the long division for, then look no further.

The widget tool is taken from the selection of tools that appears on my live worksheet app entitled Surds, Polyomials and the Remainder Theorem, that appears on my developer page.

Hope it proves helpful.

Cheers,

Mark

## Laplace Transforms Calculator

Hi Guys,

Enter a function and this evaluates the Laplace Transform or the Inverse Laplace Transform. It basically does just what it says on the tin. So if you have Laplace Transform questions that you need to work on, then look no further.

The widget tool is taken from the selection of tools that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

## Inverse Function Calculator

Hi Guys,

Enter any function and this works out the inverse along with plotting both the function and its inverse superimposed over each other. It basically does just what it says on the tin. So if you have homework that you need to check the answers for, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

Enter any function and this works out the inverse along with plotting both the function and its inverse superimposed over each other. It basically does just what it says on the tin. So if you have homework that you need to check the answers for, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

## Simplify Algebra Calculator

Hi Guys,

Enter any algebraic expression and this simplies it. It basically does just what it says on the tin. So if you have homework that you need to check, then look no further.

The widget tool is taken from the selection of tools that appears on my live worksheet app that appears on my developer page.

Hope it proves helpful.

Cheers,

Mark

Enter any algebraic expression and this simplies it. It basically does just what it says on the tin. So if you have homework that you need to check, then look no further.

The widget tool is taken from the selection of tools that appears on my live worksheet app that appears on my developer page.

Hope it proves helpful.

Cheers,

Mark

## Fractions Practice

Hi Guys,

This is a Smart Worksheet on Fractions. A lot of people, both young and old, often struggle with one aspect or another of working out fractions. The sheet covers, converting improper and proper fractions, addition and subtraction as well as multiplication and division.

It is designed so that you have a go first and then click on the question to open the video solution to check you answer. There are tutorial videos interspersed in the sheet just before you try the section of questions.

There are resets and a whole host of useful tools so that you can keep a track of your progress as you work through.

Hope you enjoy and any feedback is always appreciated. Cheers, Mark

## Mean Mode Median Calculator

Hi Guys,

Enter any data set and this will calculate the mean, mode, median and range. It does just what it says on the tin. So if you have stats work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

Enter any data set and this will calculate the mean, mode, median and range. It does just what it says on the tin. So if you have stats work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

## Calculus Limit Calculator

Hi Guys,

Enter any function at any limit value and this calculates the value of the limit. And if you click on show steps it will break down the evaluation step by step. It basically does what it says on the tin. So if you have homework that you need to check the answers for, then look no further.

Hope it proves helpful.

Cheers,

Mark

Enter any function at any limit value and this calculates the value of the limit. And if you click on show steps it will break down the evaluation step by step. It basically does what it says on the tin. So if you have homework that you need to check the answers for, then look no further.

Hope it proves helpful.

Cheers,

Mark

## Max Domain & Range Calculator

Hi Guys,

Enter any function this will calculate the maximum domain and range. It does just what it says on the tin. So if you have work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

Enter any function this will calculate the maximum domain and range. It does just what it says on the tin. So if you have work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

## Integral Calculator

Hi Guys,

Enter any integral function and this will calculate the answer. It does just what it says on the tin. So if you have integration work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

Enter any integral function and this will calculate the answer. It does just what it says on the tin. So if you have integration work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

## Partial Fractions Calculator

Hi Guys,

Enter any partial fraction functions and this generates the solution with a step by step outline solution. It basically does just what it says on the tin. So if you have homework that you need to check out, then look no further.

This tool is taken from the selection of tools that appears on my live worksheet app on Differentiation, that appears on my developer page.

Hope it proves helpful.

Cheers,

Mark

## Fourier Series Calculator

Hi Guys,

Enter any value for f(x) and value for L and this works out the Fourier Series Coefficients. It does just what it says on the tin. So if you have homework that you need to double check, then look no further.

The widget tool is taken from the selection of tools that appears on my Wolframalpha Developer Page.

Hope it proves helpful.

Cheers,

Mark

## Simplify Expression Calculator

Hi Guys,

Enter an equation or expression and this simplifies it often giving multiple versions. It basically does just what it says on the tin. So if you have homework that you need to check, then look no further.

The widget tool is taken from the selection of tools that appears on my live worksheet apps on my developer page.

Hope it proves helpful.

Cheers,

Mark

Enter an equation or expression and this simplifies it often giving multiple versions. It basically does just what it says on the tin. So if you have homework that you need to check, then look no further.

The widget tool is taken from the selection of tools that appears on my live worksheet apps on my developer page.

Hope it proves helpful.

Cheers,

Mark

## Sigma Notation sum Calculator

Hi Guys,

Enter any sigma sum and this calculates the answer. It does just what it says on the tin. So if you have work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

Enter any sigma sum and this calculates the answer. It does just what it says on the tin. So if you have work that you need to double check, then look no further.

The tool is taken from the selection of tools that appears on my live worksheet app that appears on my wolfram alpha developer page.

Hope it proves helpful.

Cheers,

Mark

## Differential Equations I

Hi Guys, This is a Smart Worksheet on First Order Differential Equations including separable, homogeneous, Integrating Factor and Bernoulli.

The worksheet also contains an array of tools so that you can type in first order d.e. problems of your own.

A pdf file is also downloadable for those who prefer to work on the worksheet independently.

Hope you enjoy it and any feedback is always appreciated.

Cheers, Mark