[[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.0423392 (sec), leaf count = 17
Maple ✓
cpu = 0.011 (sec), leaf count = 24
DSolve[Tan[y[x]] + (x + y[x])*y'[x] == 0,y[x],x]
Mathematica raw output
Solve[x + Cot[y[x]] + y[x] == C[1]*Csc[y[x]], y[x]]
Maple raw input
dsolve((x+y(x))*diff(y(x),x)+tan(y(x)) = 0, y(x),'implicit')
Maple raw output
((x+y(x))*sin(y(x))-_C1+cos(y(x)))/sin(y(x)) = 0