Comando RisolviEDO

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RisolviEDO[ <f(x,y)>, <x iniziale>, <y iniziale>, <x finale>, <Passo> ]
Risolve equazioni differenziali ordinarie di primo ordine (EDO)

\begin{equation}\frac{dy}{dx}=f(x,y) \end{equation} numericamente, dati i punti iniziale e finale e un Passo per la x. Ad esempio, per risolvere \begin{equation} \frac{dy}{dx}=-xy \end{equation} utilizzando A come punto iniziale, digitare RisolviEDO[-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 ] ]
RisolviEDO[ <f(x,y)>, <g(x,y)>, <x iniziale>, <y iniziale>, <End t>, <Passo> ]
Risolve una EDO di primo ordine

\begin{equation} \frac{dy}{dx}=\frac{f(x,y)}{g(x,y)} \end{equation} given start point, maximal value of t and Passo 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 come punto iniziale, enter RisolviEDO[-x, y, x(A), y(A), 5, 0.1]

RisolviEDO[ <b(x)>, <c(x)>, <f(x)>, <x iniziale>, <y iniziale>, <y iniziale'>, <x finale>, <Passo>]
Risolve second order EDO

\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

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

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

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

RisolviEDO(<f( var1, var2)>, <var1>, <var2>)
As above, but function f can be in variables other than x & y
RisolviEDO[ <f'(x,y)>, <x iniziale>, <y iniziale>, <x finale>, <Passo> ]
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RisolviEDO[ <y'>, <x'>, <x iniziale>, <y iniziale>, <t finale>, <Passo> ]
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RisolviEDO[ <b(x)>, <c(x)>, <f(x)>, <x iniziale>, <y iniziale>, <y' iniziale>, <x finale>, <Passo> ]
Some content was not yet translated. See the English original. Please edit the manual page if you have the rights for translation.
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