How to solve this non-linear differential equation? I'm trying to solve this non-linear differential equation using substitution $\dfrac{y}{x}$ to $t$. However, I can't solve this equation.
$$
\text{xy$\prime $} = \left(\frac{y}{x}\right)^3+y
$$
How to solve this equation and what's the general solution?
Thanks.

Here is my solution. Is this right? 
\begin{align}
\text{xy$\prime $} = \left(\frac{y}{x}\right)^3+y \\ \\
\frac{y}{x}=u, \\
y = \text{ux}, \\
\text{y$\prime $} = \text{u$\prime $x} + u \\ \\
x^2\text{u$\prime $} = u^3 \\
\int \frac{1}{u^3} \, du =\int \frac{1}{x^2} \, dx \\
-\frac{1}{2u^2} = -\frac{1}{x} + c \\
u^{2 }= \frac{1}{\frac{2}{x}+c} \\
y^{2 }= \frac{x^2}{\frac{2}{x}+c} \\
y = x\left(\frac{2}{x}+c\right)^{-\frac{1}{2}}
\end{align}
