Difference between revisions of "SolveODE Command"
From GeoGebra Manual
Line 1: | Line 1: | ||
<noinclude>{{Manual Page|version=4.0}}</noinclude> | <noinclude>{{Manual Page|version=4.0}}</noinclude> | ||
{{command|cas=true|function}} | {{command|cas=true|function}} | ||
− | ;SolveODE[ <f | + | ;SolveODE[ <f(x,y)>, <Start x>, <Start y>, <End x>, <Step> ] |
− | :Solves first order ordinary differential equations (ODE) <math>\frac{dy}{dx}=f | + | :Solves first order ordinary differential equations (ODE) <math>\frac{dy}{dx}=f(x,y)</math> numerically given start point and end & step for ''x''. |
:For example to solve <math>\frac{dy}{dx}=-xy</math> using ''A'' as a starting point, enter SolveODE[-x*y, x(A), y(A), 5, 0.1] | :For example to solve <math>\frac{dy}{dx}=-xy</math> using ''A'' as a starting point, enter SolveODE[-x*y, x(A), y(A), 5, 0.1] | ||
:{{note| 1=[[Length Command|Length]][ <Locus> ] allows you to find out how many points are in the computed locus and [[First Command|First]][ <Locus>, <Number> ] allows you to extract the points as a list, for example First[loc1, Length[loc1]].}} | :{{note| 1=[[Length Command|Length]][ <Locus> ] allows you to find out how many points are in the computed locus and [[First Command|First]][ <Locus>, <Number> ] allows you to extract the points as a list, for example First[loc1, Length[loc1]].}} |
Revision as of 19:41, 13 May 2012
- 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: To find the "reverse" solution, just enter a negative value for End x, eg SolveODE[-x*y, x(A), y(A), -5, 0.1]
- 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].
- Note: To find the "reverse" solution, just enter a negative value for End t, eg 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 currently 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}(x)=f(x, y(x)).
- Example:
SolveODE[y / x]
yields y = c1 x.
- SolveODE[ <f(v, w)>, <Dependent Variable v>, <Independent Variable w> ]
- Attempts to find the exact solution of the first order ODE \frac{dv}{dw}(w)=f(w, v(w)).
- Example:
SolveODE[y / x, y, x]
yields y = c1 x.