Difference between revisions of "SolveODE Command"
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==Outside CAS== | ==Outside CAS== | ||
; SolveODE[ <f'(x,y)>, <Start x>, <Start y>, <End x>, <Step> ] | ; SolveODE[ <f'(x,y)>, <Start x>, <Start y>, <End x>, <Step> ] | ||
| − | :Solves first order ODE given df/dx, start point and step for ''x''. | + | :Solves first order ODE ''f(x,y)=0'' given ''df/dx'', start point and step for ''x''. |
; SolveODE[ <y'>, <x'>, <Start x>, <Start y>, <End t>, <Step> ] | ; SolveODE[ <y'>, <x'>, <Start x>, <Start y>, <End t>, <Step> ] | ||
| − | :Solves first order ODE given dy/dt, dx/dt, start point, maximal value of ''t'' and step for ''t''. | + | :Solves first order ODE ''f(x(t),y(t))=0'' given ''dy/dt, dx/dt'', start point, maximal value of ''t'' and step for ''t''. |
;SolveODE[ <b(x)>, <c(x)>, <f(x)>, <Start x>, <Start y>, <Start y'>, <End x>, <Step>] | ;SolveODE[ <b(x)>, <c(x)>, <f(x)>, <Start x>, <Start y>, <Start y'>, <End x>, <Step>] | ||
:Solves second order ODE | :Solves second order ODE | ||
\begin{equation}y''+b(x)y'+c(x)y=f(x)\end{equation} | \begin{equation}y''+b(x)y'+c(x)y=f(x)\end{equation} | ||
| − | {{Note|Always returns the result as locus.}} | + | {{Note|Always returns the result as locus. The algorithms are based on Runge-Kutta numeric methods.}} |
==In CAS== | ==In CAS== | ||
; SolveODE(<f'(x,y)>) | ; SolveODE(<f'(x,y)>) | ||
| − | :Solves first order ODE given df/dx, with Maxima only. | + | :Solves first order ODE ''f(x,y)=0'' given ''df/dx'' symbolically, works with Maxima only. |
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Revision as of 17:43, 6 June 2011
Outside CAS
- SolveODE[ <f'(x,y)>, <Start x>, <Start y>, <End x>, <Step> ]
- Solves first order ODE f(x,y)=0 given df/dx, start point and step for x.
- SolveODE[ <y'>, <x'>, <Start x>, <Start y>, <End t>, <Step> ]
- Solves first order ODE f(x(t),y(t))=0 given dy/dt, dx/dt, start point, maximal value of t and step for t.
- SolveODE[ <b(x)>, <c(x)>, <f(x)>, <Start x>, <Start y>, <Start y'>, <End x>, <Step>]
- Solves second order ODE
\begin{equation}y+b(x)y'+c(x)y=f(x)\end{equation}
Note: Always returns the result as locus. The algorithms are based on Runge-Kutta numeric methods.
In CAS
- SolveODE(<f'(x,y)>)
- Solves first order ODE f(x,y)=0 given df/dx symbolically, works with Maxima only.
