4.15.46 $y^{\prime }(x)((y(x)+x)\tan (y(x))+1)+1=0$

ODE
$$y^{\prime }(x)((y(x)+x)\tan (y(x))+1)+1=0$$ ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.084345 (sec), leaf count = 14

$$\text{Solve}[y(x)+x=c_1\cos (y(x)),y(x)]$$

Maple ✓
cpu = 0.066 (sec), leaf count = 13

$$\{x+y\left(x\right)-\cos \left(y\left(x\right)\right)\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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),'implicit')

Maple raw output

x+y(x)-cos(y(x))*_C1 = 0