Internal problem ID [3988]
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]
\[ \boxed {y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 113
dsolve(diff(y(x),x)*(1+sinh(x))*sinh(y(x))+cosh(x)*(cosh(y(x))-1) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -2 \,\operatorname {arctanh}\left (\frac {\sqrt {-\frac {2 \left (2 c_{1} {\mathrm e}^{x}+c_{1} {\mathrm e}^{2 x}-2 \,{\mathrm e}^{x}-c_{1} \right ) {\mathrm e}^{x}}{c_{1}^{2}}}}{-{\mathrm e}^{2 x}+\frac {2 \,{\mathrm e}^{x}}{c_{1}}-2 \,{\mathrm e}^{x}+1}\right ) y \left (x \right ) = 2 \,\operatorname {arctanh}\left (\frac {\sqrt {-\frac {2 \left (2 c_{1} {\mathrm e}^{x}+c_{1} {\mathrm e}^{2 x}-2 \,{\mathrm e}^{x}-c_{1} \right ) {\mathrm e}^{x}}{c_{1}^{2}}}}{-{\mathrm e}^{2 x}+\frac {2 \,{\mathrm e}^{x}}{c_{1}}-2 \,{\mathrm e}^{x}+1}\right ) \end{align*}
✓ Solution by Mathematica
Time used: 10.351 (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 \text {arcsinh}\left (\frac {c_1}{4 \sqrt {\sinh (x)+1}}\right ) y(x)\to 0 \end{align*}