Internal problem ID [3987]
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]
\[ \boxed {\left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.11 (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)
\[ y \left (x \right ) = \frac {\left (-x \,{\mathrm e}^{2 \operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x} x -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}\right )}-2 c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x} x -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}\right )+x}+{\mathrm e}^{2 x} x \right ) {\mathrm e}^{-\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x} x -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}\right )}}{{\mathrm e}^{2 x}-1} \]
✓ Solution by Mathematica
Time used: 0.349 (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]
\[ \text {Solve}[x \sinh (y(x))+y(x) \sinh (x)=c_1,y(x)] \]