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 = 0.473028 (sec), leaf count = 19
\[\left \{\left \{y(x)\to \tan ^{-1}\left (x^2+\frac {c_1}{2 x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.522 (sec), leaf count = 16
\[\left [y \left (x \right ) = \arctan \left (\frac {x^{3}+2 \textit {\_C1}}{x}\right )\right ]\] 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))
Maple raw output
[y(x) = arctan((x^3+2*_C1)/x)]