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