Difference between revisions of "SolveODE Command"

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:Solves first order ODE
 
:Solves first order ODE
 
\begin{equation} \frac{dy}{dx}=\frac{f(x,y)}{g(x,y)} \end{equation}
 
\begin{equation} \frac{dy}{dx}=\frac{f(x,y)}{g(x,y)} \end{equation}
given start point, maximal value of ''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.
+
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
 
For example to solve
 
\begin{equation}\frac{dy}{dx}=- \frac{x}{y} \end{equation}
 
\begin{equation}\frac{dy}{dx}=- \frac{x}{y} \end{equation}

Revision as of 06:11, 9 August 2011



SolveODE[ <f'(x,y)>, <Start x>, <Start y>, <End x>, <Step> ]
Solves first order ordinary differential equations (ODE)

\begin{equation}\frac{dy}{dx}=f'(x,y) \end{equation} numerically given start point and end & step for x. For example to solve \begin{equation} \frac{dy}{dx}=-xy \end{equation} 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

\begin{equation} \frac{dy}{dx}=\frac{f(x,y)}{g(x,y)} \end{equation} 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 \begin{equation}\frac{dy}{dx}=- \frac{x}{y} \end{equation} 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

\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.

CAS Syntax

Following two syntaxes work only in CAS View and only with Maxima as CAS.

SolveODE(<f(x,y)>)
Attempts to find the exact solution of the first order ODE

\begin{equation} \frac{dy}{dx}=f(x,y) \end{equation}

SolveODE(<f( var1, var2)>, <var1>, <var2>)
As above, but function f can be in variables other than x & y
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