Differential Equations

Using the GeoGebra command solveODE you can illustrate numerical solutions to first and second order ordinary differential equations.

First order differential equations

When using the command solveODE $$y$$ must be a function of $$x$$. Let

$\frac{dy}{dx} = f(x,y)$

then you can used the commands:

solveODE[f]
solveODE[f, <Point on f>]
solveODE[f, <Start x>, <Start y>, <End x>, <Step>]


and:

SlopeField[f]
SlopeField[f, <Number n>]
SlopeField[f, <Number n>, <Length multiplier a>]


If the solution curve has vertical points and if the equation can be written as

$\frac{dy}{dx} = \frac{f(x,y)}{g(x,y)}$

it is better to use the command

solveODE[f, g, x(A), y(A), <End t>, <Step> ]


where A is a point on the curve. This command is used in the worksheet above.

Second order differential equations

The command

SolveODE[ <b(x)>, <c(x)>, <f(x)>, <Start x>, <Start y>, <Start y'>, <End x>, <Step> ]


solves the equation

$y''+b(x)y'+c(x)y=f(x)$

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License

www.malinc.se