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