4.15.50 $y^{\prime }(x)(x\cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x)\cosh (x)=0$

ODE
$$y^{\prime }(x)(x\cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x)\cosh (x)=0$$ ODE Classification

[_exact]

Book solution method
Exact equation

Mathematica ✓
cpu = 0.0571608 (sec), leaf count = 17

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

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

$$\{\sinh \left(x\right)y\left(x\right)+x\sinh \left(y\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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