ODE
\[ (y(x)+x) y'(x)+\tan (y(x))=0 \] ODE Classification
[[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.0423392 (sec), leaf count = 17
\[\text {Solve}\left [y(x)+\cot (y(x))+x=c_1 \csc (y(x)),y(x)\right ]\]
Maple ✓
cpu = 0.011 (sec), leaf count = 24
\[ \left \{ {\frac { \left ( x+y \left ( x \right ) \right ) \sin \left ( y \left ( x \right ) \right ) -{\it \_C1}+\cos \left ( y \left ( x \right ) \right ) }{\sin \left ( y \left ( x \right ) \right ) }}=0 \right \} \] Mathematica raw input
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