4.10.27 \(y'(x) (\tan (x) \sec (x)-2 y(x))+\sec (x) (2 y(x) \sin (x)+1)=0\)

ODE
\[ y'(x) (\tan (x) \sec (x)-2 y(x))+\sec (x) (2 y(x) \sin (x)+1)=0 \] ODE Classification

[[_Abel, `2nd type``class A`]]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 64.6074 (sec), leaf count = 0 , could not solve

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

Maple
cpu = 37.955 (sec), leaf count = 0 , could not solve

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

Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

dsolve((tan(x)*sec(x)-2*y(x))*diff(y(x),x)+sec(x)*(1+2*y(x)*sin(x)) = 0, y(x),'i
mplicit')