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),'implicit')