4.15.44 $y^{\prime }(x)(x^2+2y(x)\sin (x)\sec (y(x)))+2x\tan (y(x))+y(x{)}^2\cos (x)\sec (y(x))=0$

ODE
$$y^{\prime }(x)(x^2+2y(x)\sin (x)\sec (y(x)))+2x\tan (y(x))+y(x{)}^2\cos (x)\sec (y(x))=0$$ ODE Classification

[NONE]

Book solution method
Exact equation, integrating factor

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

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

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

$$\{{\left(y\left(x\right)\right)}^2\sin \left(x\right)+x^2\sin \left(y\left(x\right)\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ 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