4.15.43 $y^{\prime }(x)(\cos (x)\sec (y(x))+x)+\tan (y(x))-y(x)\sin (x)\sec (y(x))=0$

ODE
$$y^{\prime }(x)(\cos (x)\sec (y(x))+x)+\tan (y(x))-y(x)\sin (x)\sec (y(x))=0$$ ODE Classification

[NONE]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.0577803 (sec), leaf count = 17

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

Maple ✓
cpu = 0.08 (sec), leaf count = 15

$$\{y\left(x\right)\cos \left(x\right)+\sin \left(y\left(x\right)\right)x+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[Tan[y[x]] - Sec[y[x]]*Sin[x]*y[x] + (x + Cos[x]*Sec[y[x]])*y'[x] == 0,y[x],x]

Mathematica raw output

Solve[C[1] == x*Sin[y[x]] + Cos[x]*y[x], y[x]]

Maple raw input

dsolve((x+cos(x)*sec(y(x)))*diff(y(x),x)+tan(y(x))-y(x)*sin(x)*sec(y(x)) = 0, y(x),'implicit')

Maple raw output

y(x)*cos(x)+sin(y(x))*x+_C1 = 0