Internal problem ID [3480]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 747.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \left (1+\sinh \relax (x )\right ) \sinh \relax (y)+\cosh \relax (x ) \left (\cosh \relax (y)-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve(diff(y(x),x)*(1+sinh(x))*sinh(y(x))+cosh(x)*(cosh(y(x))-1) = 0,y(x), singsol=all)
\[ y \relax (x ) = \mathrm {arccosh}\left (\frac {{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}+\frac {2 \,{\mathrm e}^{x}}{c_{1}}-1}{{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-1}\right ) \]
✓ Solution by Mathematica
Time used: 5.907 (sec). Leaf size: 32
DSolve[y'[x](1+Sinh[x])Sinh[y[x]]+Cosh[x](Cosh[y[x]]-1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to 2 \sinh ^{-1}\left (\frac {c_1}{4 \sqrt {\sinh (x)+1}}\right ) \\ y(x)\to 0 \\ \end{align*}