ODE
\[ x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right ) \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of Variable, new dependent variable
Mathematica ✓
cpu = 0.466701 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \tan ^{-1}\left (\frac {\log (x)+4 c_1}{x^2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.535 (sec), leaf count = 15
\[\left [y \left (x \right ) = \arctan \left (\frac {\ln \left (x \right )-\textit {\_C1}}{x^{2}}\right )\right ]\] Mathematica raw input
DSolve[x^3*y'[x] == Cos[y[x]]*(Cos[y[x]] - 2*x^2*Sin[y[x]]),y[x],x]
Mathematica raw output
{{y[x] -> ArcTan[(4*C[1] + Log[x])/x^2]}}
Maple raw input
dsolve(x^3*diff(y(x),x) = cos(y(x))*(cos(y(x))-2*x^2*sin(y(x))), y(x))
Maple raw output
[y(x) = arctan((ln(x)-_C1)/x^2)]