4.15.44 \(y'(x) \left (x^2+2 y(x) \sin (x) \sec (y(x))\right )+2 x \tan (y(x))+y(x)^2 \cos (x) \sec (y(x))=0\)

ODE
\[ y'(x) \left (x^2+2 y(x) \sin (x) \sec (y(x))\right )+2 x \tan (y(x))+y(x)^2 \cos (x) \sec (y(x))=0 \] ODE Classification

[NONE]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0705649 (sec), leaf count = 21

\[\text {Solve}\left [c_1=x^2 \sin (y(x))+y(x)^2 \sin (x),y(x)\right ]\]

Maple
cpu = 0.105 (sec), leaf count = 19

\[ \left \{ \left (y \relax (x ) \right ) ^{2}\sin \relax (x ) +{x}^{2}\sin \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

Solve[C[1] == x^2*Sin[y[x]] + Sin[x]*y[x]^2, y[x]]

Maple raw input

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

Maple raw output

y(x)^2*sin(x)+x^2*sin(y(x))+_C1 = 0