Visualizing the Solution of Two Linear Differential Equations

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The analytical solutions of the two differential equations and , subject to the initial conditions and are used to create two plots, a parametric plot of a curve with horizontal coordinate and vertical coordinate and a standard plot of and as functions of from 0 to .


The initial conditions and are set by locators on the parametric plot; you can use more than one. A locator's horizontal and vertical coordinates give and , respectively. After changing from the parametric plot to the standard plot, locators appear on the standard plot if and is in the plot range.


Contributed by: Mikhail Dimitrov Mikhailov (March 2011)
Open content licensed under CC BY-NC-SA



The expressions for and given by the Mathematica built-in function DSolve are not applicable when . For this special case the solutions are simplified using Mathematica's Limit function. Thus our function twoDSolve correctly computes and for all parameters specified.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.