29.26.10 problem 746

Internal problem ID [5331]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 746
Date solved : Monday, January 27, 2025 at 11:14:55 AM
CAS classification : [_exact]

\begin{align*} \left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.286 (sec). Leaf size: 180

dsolve((sinh(x)+x*cosh(y(x)))*diff(y(x),x)+y(x)*cosh(x)+sinh(y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\left (2 c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{2 x +\textit {\_Z}}-x \,{\mathrm e}^{2 x +\textit {\_Z}}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x} x -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x \right )+x}+x \left ({\mathrm e}^{2 \operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{2 x +\textit {\_Z}}-x \,{\mathrm e}^{2 x +\textit {\_Z}}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x} x -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x \right )}-{\mathrm e}^{2 x}\right )\right ) {\mathrm e}^{-\operatorname {RootOf}\left (\textit {\_Z} \,{\mathrm e}^{2 x +\textit {\_Z}}-x \,{\mathrm e}^{2 x +\textit {\_Z}}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{x +\textit {\_Z}}-{\mathrm e}^{2 x} x -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x \right )}}{{\mathrm e}^{2 x}-1} \]

✓ Solution by Mathematica

Time used: 0.227 (sec). Leaf size: 17

DSolve[(Sinh[x]+x*Cosh[y[x]])*D[y[x],x]+y[x]*Cosh[x]+Sinh[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[x \sinh (y(x))+y(x) \sinh (x)=c_1,y(x)] \]