4.15.46 \(y'(x) ((y(x)+x) \tan (y(x))+1)+1=0\)

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

\[ \left \{ x+y \relax (x ) -\cos \left (y \relax (x ) \right ) {\it \_C1}=0 \right \} \] 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