Initial Conditions - Maple Help

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Initial Conditions

 Calling Sequence initialcondition[function name](eqn_1,eqn_2,...) function(args)

Parameters

 eqn_n - equation or set of equations defining a system function - function name used to construct the initial condition

Description

 • The initialcondition routine can be used to augment a set of equations with additional equations defining the initial conditions for the given system.
 • The set of equations is formed from the arguments to the procedure. This set is further augmented by a new equation of the form ${\mathrm{D}}^{\left(n\right)}\left(f\right)\left(a\right)=b$ if derivatives are present, or $f\left(a\right)=b$ otherwise.

Examples

 > $\mathrm{initialcondition}\left(\left\{{x}^{2}+{y}^{2}=1,{x}^{3}-{y}^{2}x+xy=3\right\}\right)$
 $\left\{{{x}}^{{2}}{+}{{y}}^{{2}}{=}{1}{,}{{x}}^{{3}}{-}{x}{}{{y}}^{{2}}{+}{x}{}{y}{=}{3}{,}{\mathrm{f0}}{}\left({0}\right){=}{\mathrm{a0}}\right\}$ (1)
 > $\mathrm{initialcondition}[f]\left(\frac{{{ⅆ}}^{2}}{{ⅆ}{x}^{2}}f\left(x\right)=\mathrm{sin}\left(x\right)\right)$
 $\left\{\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{f}{}\left({x}\right){=}{\mathrm{sin}}{}\left({x}\right){,}{{\mathrm{D}}}^{\left({\mathrm{n1}}\right)}{}\left({f}\right){}\left({0}\right){=}{0}\right\}$ (2)