SolveODE Command

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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


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.

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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