##### 4.15.50 $$y'(x) (x \cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x) \cosh (x)=0$$

ODE
$y'(x) (x \cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x) \cosh (x)=0$ ODE Classiﬁcation

[_exact]

Book solution method
Exact equation

Mathematica
cpu = 0.455733 (sec), leaf count = 17

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

Maple
cpu = 0.499 (sec), leaf count = 179

$\left [y \left (x \right ) = \frac {\left (-x \,{\mathrm e}^{2 \RootOf \left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 \textit {\_C1} \,{\mathrm e}^{\textit {\_Z} +x}-{\mathrm e}^{2 x} x -{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +x \,{\mathrm e}^{\textit {\_Z}}\right )}-2 \textit {\_C1} \,{\mathrm e}^{\RootOf \left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 \textit {\_C1} \,{\mathrm e}^{\textit {\_Z} +x}-{\mathrm e}^{2 x} x -{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +x \,{\mathrm e}^{\textit {\_Z}}\right )+x}+{\mathrm e}^{2 x} x \right ) {\mathrm e}^{-\RootOf \left (\textit {\_Z} \,{\mathrm e}^{\textit {\_Z} +2 x}-x \,{\mathrm e}^{\textit {\_Z} +2 x}+x \,{\mathrm e}^{2 \textit {\_Z}}+2 \textit {\_C1} \,{\mathrm e}^{\textit {\_Z} +x}-{\mathrm e}^{2 x} x -{\mathrm e}^{\textit {\_Z}} \textit {\_Z} +x \,{\mathrm e}^{\textit {\_Z}}\right )}}{{\mathrm e}^{2 x}-1}\right ]$ Mathematica raw input

DSolve[Sinh[y[x]] + Cosh[x]*y[x] + (x*Cosh[y[x]] + Sinh[x])*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[C[1] == x*Sinh[y[x]] + Sinh[x]*y[x], y[x]]

Maple raw input

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

Maple raw output

[y(x) = (-x*exp(RootOf(_Z*exp(_Z+2*x)-x*exp(_Z+2*x)+x*exp(_Z)^2+2*_C1*exp(_Z+x)-
exp(x)^2*x-exp(_Z)*_Z+x*exp(_Z)))^2-2*_C1*exp(RootOf(_Z*exp(_Z+2*x)-x*exp(_Z+2*x
)+x*exp(_Z)^2+2*_C1*exp(_Z+x)-exp(x)^2*x-exp(_Z)*_Z+x*exp(_Z))+x)+exp(x)^2*x)/ex
p(RootOf(_Z*exp(_Z+2*x)-x*exp(_Z+2*x)+x*exp(_Z)^2+2*_C1*exp(_Z+x)-exp(x)^2*x-exp
(_Z)*_Z+x*exp(_Z)))/(exp(x)^2-1)]