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