ODE
\[ y'(x) ((y(x)+x) \tan (y(x))+1)+1=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.084345 (sec), leaf count = 14
\[\text {Solve}\left [y(x)+x=c_1 \cos (y(x)),y(x)\right ]\]
Maple ✓
cpu = 0.066 (sec), leaf count = 13
\[ \left \{ x+y \left ( x \right ) -\cos \left ( y \left ( x \right ) \right ) {\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[1 + (1 + Tan[y[x]]*(x + y[x]))*y'[x] == 0,y[x],x]
Mathematica raw output
Solve[x + y[x] == C[1]*Cos[y[x]], y[x]]
Maple raw input
dsolve((1+(x+y(x))*tan(y(x)))*diff(y(x),x)+1 = 0, y(x),'implicit')
Maple raw output
x+y(x)-cos(y(x))*_C1 = 0