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 = 0.0571608 (sec), leaf count = 17

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

Maple
cpu = 0.071 (sec), leaf count = 15

\[ \left \{ \sinh \relax (x ) y \relax (x ) +x\sinh \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

sinh(x)*y(x)+x*sinh(y(x))+_C1 = 0