Solve the equation $y=2xy'+y^2y'^3$ Solve the equation $y=2xy'+y^2y'^3$.

I have tried to solve it but I can't recognize what type of equation I have learnt.
$$y=2xy'+y^2y'^3$$
Multiply by $y$
$$y^2=2xyy'+y^3y'^3$$
Substitute $y^2=u$
$$u=xu'+\frac 1 8(u')^3$$
It's Clairaut 's equation
$$y=xy'+g(y')$$
And the general solution is given by
$$u(x)=Cx+\frac {C^3}{8}$$
$$y^2(x)=Cx+\frac {C^3}{8}$$
Maple dsolve(eq,implicit) gives solutions
$$\left( y \left( x \right)  \right) ^{4}+{\frac {32\,{x}^{3}}{27}}=0$$
$$x \left( {\it \_T} \right) ={-\frac { \left( {\it \_C1}\,{{\it 
\_T}}^{2}-1 \right) {\it \_C1}}{{2{\it \_T}}^{2}}},\;y \left( {\it \_T}
 \right) ={\frac {{\it \_C1}}{{\it \_T}}}
$$