Wolfram Demonstrations Project

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.

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.

Embed Interactive Demonstration New!

RELATED RESOURCES

Mathematica » The #1 tool for creating Demonstrations and anything technical.	Wolfram\|Alpha » Explore anything with the first computational knowledge engine.	MathWorld » The web's most extensive mathematics resource.	Course Assistant Apps » An app for every course— right in the palm of your hand.
Wolfram Blog » Read our views on math, science, and technology.	Computable Document Format » The format that makes Demonstrations (and any information) easy to share and interact with.	STEM Initiative » Programs & resources for educators, schools & students.	Computerbasedmath.org » Join the initiative for modernizing math education.

Visualizing the Solution of Two Linear Differential Equations