Internal problem ID [3479]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 746.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left (\sinh \relax (x )+x \cosh \relax (y)\right ) y^{\prime }+y \cosh \relax (x )+\sinh \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.703 (sec). Leaf size: 179
dsolve((sinh(x)+x*cosh(y(x)))*diff(y(x),x)+y(x)*cosh(x)+sinh(y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-x \,{\mathrm e}^{2 \RootOf \left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-x \,{\mathrm e}^{2 x}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x \right )}-2 c_{1} {\mathrm e}^{\RootOf \left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-x \,{\mathrm e}^{2 x}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x \right )+x}+x \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-\RootOf \left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-x \,{\mathrm e}^{2 x}-\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x \right )}}{{\mathrm e}^{2 x}-1} \]
✓ Solution by Mathematica
Time used: 0.211 (sec). Leaf size: 17
DSolve[(Sinh[x]+x Cosh[y[x]])y'[x]+y[x] Cosh[x]+Sinh[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[x \sinh (y(x))+y(x) \sinh (x)=c_1,y(x)] \]