Solve a System of Partial Differential Equations - Maple Help

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Solve a System of Partial Differential Equations

 Description Solve a system of partial differential equations (PDEs).

Enter a system of PDEs.

 >
 $\left[{-}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{r}}^{{2}}}{}{F}{}\left({r}{,}{s}\right)\right){+}\frac{{{\partial }}^{{2}}}{{\partial }{{s}}^{{2}}}{}{F}{}\left({r}{,}{s}\right){+}\frac{{ⅆ}}{{ⅆ}{r}}{}{H}{}\left({r}\right){+}\frac{{ⅆ}}{{ⅆ}{s}}{}{G}{}\left({s}\right){+}{s}{=}{0}{,}\frac{{{\partial }}^{{2}}}{{\partial }{{r}}^{{2}}}{}{F}{}\left({r}{,}{s}\right){+}\frac{{{\partial }}^{{2}}}{{\partial }{s}{}{\partial }{r}}{}{F}{}\left({r}{,}{s}\right){+}\frac{{{\partial }}^{{2}}}{{\partial }{{s}}^{{2}}}{}{F}{}\left({r}{,}{s}\right){-}\left(\frac{{ⅆ}}{{ⅆ}{r}}{}{H}{}\left({r}\right)\right){+}\frac{{ⅆ}}{{ⅆ}{s}}{}{G}{}\left({s}\right){-}{r}{=}{0}\right]$ (1)

Solve the system of PDEs.

 > $\mathrm{pdsolve}\left(\right)$
 $\left\{{F}{}\left({r}{,}{s}\right){=}{\mathrm{_F2}}{}\left({s}\right){+}{\mathrm{_F3}}{}\left({r}\right){+}\frac{{1}}{{6}}{}{{r}}^{{2}}{}{s}{+}\frac{{1}}{{6}}{}\left({{s}}^{{2}}{+}{6}{}{\mathrm{_C1}}{}{s}{+}{6}{}{\mathrm{_C2}}\right){}{r}{,}{G}{}\left({s}\right){=}{-}\frac{{1}}{{3}}{}{{s}}^{{2}}{-}\left(\frac{{ⅆ}}{{ⅆ}{s}}{}{\mathrm{_F2}}{}\left({s}\right)\right){-}\frac{{1}}{{2}}{}{\mathrm{_C1}}{}{s}{+}{\mathrm{_C4}}{,}{H}{}\left({r}\right){=}\frac{{ⅆ}}{{ⅆ}{r}}{}{\mathrm{_F3}}{}\left({r}\right){-}\frac{{1}}{{6}}{}{{r}}^{{2}}{+}\frac{{1}}{{2}}{}{\mathrm{_C1}}{}{r}{+}{\mathrm{_C3}}\right\}$ (2)
 Commands Used