4.15.39 $$y'(x) \left (x^2 \sec (x) \cos (y(x))+1\right )-y(x) \tan (x)+\sec (x) \sin (y(x))=0$$

ODE
$y'(x) \left (x^2 \sec (x) \cos (y(x))+1\right )-y(x) \tan (x)+\sec (x) \sin (y(x))=0$ ODE Classiﬁcation

[NONE]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 8.66776 (sec), leaf count = 0 , could not solve

DSolve[Sec[x]*Sin[y[x]] - Tan[x]*y[x] + (1 + x^2*Cos[y[x]]*Sec[x])*Derivative[1][y][x] == 0, y[x], x]

Maple
cpu = 183.428 (sec), leaf count = 0 , could not solve

dsolve((1+x^2*sec(x)*cos(y(x)))*diff(y(x),x)-y(x)*tan(x)+sec(x)*sin(y(x)) = 0, y(x))

Mathematica raw input

DSolve[Sec[x]*Sin[y[x]] - Tan[x]*y[x] + (1 + x^2*Cos[y[x]]*Sec[x])*y'[x] == 0,y[x],x]

Mathematica raw output

DSolve[Sec[x]*Sin[y[x]] - Tan[x]*y[x] + (1 + x^2*Cos[y[x]]*Sec[x])*Derivative[1]
[y][x] == 0, y[x], x]

Maple raw input

dsolve((1+x^2*sec(x)*cos(y(x)))*diff(y(x),x)-y(x)*tan(x)+sec(x)*sin(y(x)) = 0, y(x))

Maple raw output

dsolve((1+x^2*sec(x)*cos(y(x)))*diff(y(x),x)-y(x)*tan(x)+sec(x)*sin(y(x)) = 0, y
(x))