4.5.2 \(\cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0\)

ODE
\[ \cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0 \] ODE Classification

[`y=_G(x,y')`]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.0673996 (sec), leaf count = 19

\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {c_1}{2 x}+x^2\right )\right \}\right \}\]

Maple
cpu = 0.443 (sec), leaf count = 17

\[ \left \{ -{\it \_C1}+x\tan \left (y \relax (x ) \right ) -{x}^{3}=0 \right \} \] Mathematica raw input

DSolve[Cos[y[x]]*(-3*x^2*Cos[y[x]] + Sin[y[x]]) + x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> ArcTan[x^2 + C[1]/(2*x)]}}

Maple raw input

dsolve(x*diff(y(x),x)+(sin(y(x))-3*x^2*cos(y(x)))*cos(y(x)) = 0, y(x),'implicit')

Maple raw output

-_C1+x*tan(y(x))-x^3 = 0