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 = 0.373002 (sec), leaf count = 17
\[\text {Solve}[y(x)+\cot (y(x))+x=c_1 \csc (y(x)),y(x)]\]
Maple ✓
cpu = 0.26 (sec), leaf count = 26
\[\left [x -\frac {-\cos \left (y \left (x \right )\right )-y \left (x \right ) \sin \left (y \left (x \right )\right )+\textit {\_C1}}{\sin \left (y \left (x \right )\right )} = 0\right ]\] 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))
Maple raw output
[x-(-cos(y(x))-y(x)*sin(y(x))+_C1)/sin(y(x)) = 0]