# Differential Equations TI89 App with Step by Step Solutions

## Solve Differential Equations questions stepwise using the TI89 Calculator

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Version 10.0  -  Read the DEQME User Guide

Read a SUMMARY(pdf file) of all Functionality under F1 and F2 with many examples and screenshots and a comparison with other CAS products.

 F1:  1. Order F2:  2. Order F3:  3. Order and higher F4: Partial DEqns F5: Transforms F6: More F7:  Exit 1 Basics + Definitions Any 2. Order DiffEqn 3. Order: Linear & Constant Coefficients - Homogenous PDE-Basics LaPlace-Definition and Examples Find EigenValues and EigenVectors - Step by Step Exit 2 Any 1. order DiffEqn Homogeneous 3. Order: Linear & Constant Coefficients - Not Homogenous LaPlace Equation Solve Diff Eqn using LaPlace Transform - Step by Step Rate Problems About 3 Separable - Step by Step Non-Homogeneous 3. Order: Linear & Constant Coefficients using Variation of Parameter Diffusion Equation Do LaPlace Transform Salt in Tank - type Diff Eqns. Reset Constants to @1 4 Find Differential DiffEqn Checker Cauchy-Euler D.E. of 3. Order Wave Equation Do Inverse LaPlace Transform Find Wronskian Notes 5 Homogeneous - Step by Step IVP Solver given a) y(x1) , y'(x2) b) y'(x1) , y'(x2) c) y(x1) , y(x2) 4. Order: Linear & Constant Coefficients - Homogenous Helmholtz Equation Do Inverse LaPlace - STEPS for partial fractions and linear numerators Wronskian to find coefficients 6 Exact - Step by Step Variation of Parameter - Step by Step 2x2 Linear System: x'=a*x+b*y y'=c*x+d*y Poisson Equation Fourier Series  - Stepwise Annihilator Method 7 Non-exact - Step by Step Undetermined Coefficients - Step by Step X' = A* X Discrete Fourier Transform (DFT, FFT) Do Picard Method 8 Linear in x - Step by Step with Integrating Factor Bessel DiffEqn X' = A* X + F Table of Fourier Transforms Error Function 9 Linear in x - Step by Step using Variation of Parameter Reduction of Order Separable Diff Eqn More Transforms Phase Line A Linear in y - Step by Step with Integrating Factor Legendre DEQ Partial Fraction Decomposition (Steps) Orthogonal Trajectories B Linear in y - Step by Step using Variation of Parameter Cauchy-Euler DEQ Homogeneous Complex Partial Fraction Decomposition (Steps) C M(x,y)dx+N(x,y)dy - Step by Step Cauchy-Euler DEQ Non homogeneous Perform Convolution of f and g . D N(x,y)*y'+M(x,y)=0 - Step by Step Series Solution Infinite Binomial Series and Binomial Expansion E DiffEqn Checker Frobenius Series F RL Circuits Solve RCL Circuits G Bernoulli - Step by Step Vibrating Spring H Riccati Equation Find g(x) in y''+ay'+by=g(x) given particular solution. I Clairaut Equation J Lagrange (d'Alembert) Equation K Linear Fractions - Step by Step L Tractrix M Slope Field N Particular Solution O Euler's Method P Euler's Method Backwards Q Runge Kutta R Midpoint

 User C. F.: "The additions such as step by step exact DE, step by step homogeneous and step by step bernoulli are fantastic and would definitely make differential equations made easy an excellent study tool for anyone. Or it can be used as a quick solver to check steps. I think it's the best software of it's kind."User A.M.: I just have to give it to you guys for the great job you are doing. I was using the salt in tank program and it works flawlessly, its beyond everything I expected. Thanks again User J. P.: I highly recommend DME, it is unlike anything else out there. The ability to solve nearly any first and second order differential equation makes almost as powerful as a computer. Great for solving HW problems and the step-by-step function helped me to find my mistakes, which makes it better than a computer!  I love the phase line tool and the step-by-step Inverse LaPlace function.  It is a great learning tool. – modem designer

2.2  Separable Differential Equations Module

 Option# in head menu F1: Enter DEQ F2: Solve DEQ F3: Steps F4: Compute F5: Graph F6: Euler F6: Exit Return to main screen) 1 dy/dx = f(x,y)   Any separable Diff Eqn. Solve dy/dx = f(x,y) Show Steps Compute y(a) Graph Slope Field Approximate analyt. solution to Diff Eqn.  upon entering (x0,y0), step size and #points. 2 y'(t) = k*y(t) Exponential Growth Solve  y'(t) = k*y(t) Exponential Growth Solve y(x)=C Graph Particular Solution 3 y'(t) = k*(y(t)-A) Ex: Newton's Law of Cooling Solve y'(t) = k*(y(t)-A) Ex: Newton's Law of Cooling Tangent at x=a Clear Graph 4 y'(t) = k*(A-y(t)) Ex: Wolves problem Solve y'(t) = k*(A-y(t)) Ex: Wolves problem Find d2y/dx2 Select Window Size define xmin, xmax, ymin, ymax, # vertical and horiz. lines 5 y'(t) = k*y*(A-y) Logistic Growth Solve y'(t) = k*y*(A-y) Logistic Growth Limit x-> infinity