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 = 11.0559 (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 = 85.502 (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),'implicit')
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),'implicit')
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),'implicit')