ODE
\[ x \left (x^3+3 x^2 y(x)+y(x)^3\right ) y'(x)=y(x)^2 \left (3 x^2+y(x)^2\right ) \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.50428 (sec), leaf count = 34
\[\text {Solve}\left [\frac {y(x)^3}{3 x^3}+\frac {3 y(x)}{x}+\log \left (\frac {y(x)}{x}\right )+\log (x)=c_1,y(x)\right ]\]
Maple ✓
cpu = 0.225 (sec), leaf count = 27
\[[y \left (x \right ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{3 \textit {\_Z}}+9 \,{\mathrm e}^{\textit {\_Z}}+3 \textit {\_C1} +3 \textit {\_Z} +3 \ln \left (x \right )\right )} x]\] Mathematica raw input
DSolve[x*(x^3 + 3*x^2*y[x] + y[x]^3)*y'[x] == y[x]^2*(3*x^2 + y[x]^2),y[x],x]
Mathematica raw output
Solve[Log[x] + Log[y[x]/x] + (3*y[x])/x + y[x]^3/(3*x^3) == C[1], y[x]]
Maple raw input
dsolve(x*(x^3+3*x^2*y(x)+y(x)^3)*diff(y(x),x) = (3*x^2+y(x)^2)*y(x)^2, y(x))
Maple raw output
[y(x) = exp(RootOf(exp(_Z)^3+9*exp(_Z)+3*_C1+3*_Z+3*ln(x)))*x]