# SolveODE Command

From GeoGebra Manual

Revision as of 09:59, 25 August 2011 by Christina.biermair (talk | contribs)

- SolveODE[ <f'(x,y)>, <Start x>, <Start y>, <End x>, <Step> ]
- Solves first order ordinary differential equations (ODE) \frac{dy}{dx}=f'(x,y) numerically given start point and end & step for
*x*. - For example to solve \frac{dy}{dx}=-xy using
*A*as a starting point, enter SolveOde[-x*y, x(A), y(A), 5, 0.1]

**Note:**Length[ <Locus> ] allows you to find out how many points are in the computed locus and First[ <Locus>, <Number> ] allows you to extract the points as a list, for example First[loc1, Length[loc1]]

- SolveODE[ <f(x,y)>, <g(x,y)>, <Start x>, <Start y>, <End t>, <Step> ]
- Solves first order ODE \frac{dy}{dx}=\frac{f(x,y)}{g(x,y)} given start point, maximal value of an internal parameter
*t*and step for*t*. This version of the command may work where the first one fails eg when the solution curve has vertical points. - For example to solve \frac{dy}{dx}=- \frac{x}{y} using
*A*as a starting point, enter SolveOde[-x, y, x(A), y(A), 5, 0.1] - SolveODE[ <b(x)>, <c(x)>, <f(x)>, <Start x>, <Start y>, <Start y'>, <End x>, <Step>]
- Solves second order ODE y''+b(x)y'+c(x)y=f(x).

**Note:**Always returns the result as locus. The algorithms are based on Runge-Kutta numeric methods.

## CAS Syntax

Following two syntaxes work only in CAS View.

- SolveODE(<f(x,y)>)
- Attempts to find the exact solution of the first order ODE \frac{dy}{dx}=f(x,y).

- SolveODE(<f( var1, var2)>, <var1>, <var2>)
- Attempts to find the exact solution of the first order ODE \frac{dvar1}{dvar2}=f(var1,var2).