4.15.43 \(y'(x) (\cos (x) \sec (y(x))+x)+\tan (y(x))-y(x) \sin (x) \sec (y(x))=0\)

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

[NONE]

Book solution method
Exact equation, integrating factor

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

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

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

\[ \left \{ y \relax (x ) \cos \relax (x ) +\sin \left (y \relax (x ) \right ) x+{\it \_C1}=0 \right \} \] 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