ODE
\[ x \left (6 y(x)^2+x\right ) y'(x)-3 y(x)^3+x y(x)=0 \] ODE Classification
[[_homogeneous, `class G`], _rational]
Book solution method
Exact equation, integrating factor
Mathematica ✓
cpu = 0.372945 (sec), leaf count = 64
\[\left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{3 c_1}}{x^3}\right )}}{\sqrt {6}}\right \}\right \}\]
Maple ✓
cpu = 0.247 (sec), leaf count = 25
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{-\frac {\LambertW \left (\frac {6 \,{\mathrm e}^{3 \textit {\_C1}}}{x^{3}}\right )}{2}+\frac {3 \textit {\_C1}}{2}}}{x}\right ]\] Mathematica raw input
DSolve[x*y[x] - 3*y[x]^3 + x*(x + 6*y[x]^2)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -((Sqrt[x]*Sqrt[ProductLog[(6*E^(3*C[1]))/x^3]])/Sqrt[6])}, {y[x] -> (Sqrt[x]*Sqrt[ProductLog[(6*E^(3*C[1]))/x^3]])/Sqrt[6]}}
Maple raw input
dsolve(x*(x+6*y(x)^2)*diff(y(x),x)+x*y(x)-3*y(x)^3 = 0, y(x))
Maple raw output
[y(x) = 1/x*exp(-1/2*LambertW(6*exp(3*_C1)/x^3)+3/2*_C1)]