# 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

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