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 = 0.394492 (sec), leaf count = 14
\[\text {Solve}[y(x)+x=c_1 \cos (y(x)),y(x)]\]
Maple ✓
cpu = 0.18 (sec), leaf count = 13
\[[x -\cos \left (y \left (x \right )\right ) \textit {\_C1} +y \left (x \right ) = 0]\] 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))
Maple raw output
[x-cos(y(x))*_C1+y(x) = 0]