ODE
\[ x \left (-3 x^3 y(x)+x^3+4 y(x)^2\right ) y'(x)=6 y(x)^3 \] ODE Classification
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
Book solution method
Change of Variable, new independent variable
Mathematica ✓
cpu = 0.50031 (sec), leaf count = 27
\[\text {Solve}\left [\frac {y(x)^2}{x^3}+\frac {1}{2} (\log (y(x))-3 y(x))=c_1,y(x)\right ]\]
Maple ✓
cpu = 0.211 (sec), leaf count = 31
\[[y \left (x \right ) = {\mathrm e}^{\RootOf \left (-3 x^{3} {\mathrm e}^{\textit {\_Z}}+6 \textit {\_C1} \,x^{3}+\textit {\_Z} \,x^{3}+2 \,{\mathrm e}^{2 \textit {\_Z}}\right )}]\] Mathematica raw input
DSolve[x*(x^3 - 3*x^3*y[x] + 4*y[x]^2)*y'[x] == 6*y[x]^3,y[x],x]
Mathematica raw output
Solve[(Log[y[x]] - 3*y[x])/2 + y[x]^2/x^3 == C[1], y[x]]
Maple raw input
dsolve(x*(x^3-3*x^3*y(x)+4*y(x)^2)*diff(y(x),x) = 6*y(x)^3, y(x))
Maple raw output
[y(x) = exp(RootOf(-3*x^3*exp(_Z)+6*_C1*x^3+_Z*x^3+2*exp(_Z)^2))]