General solution of $x^{ 2 }\left( y-x\frac { dy }{ dx } \right) =y{ \left( \frac { dy }{ dx } \right) }^{ 2 }$ Find the general solution of the differential equation
$${ x }^{ 2 }\left( y-x\dfrac { dy }{ dx }  \right) =y{ \left( \dfrac { dy }{ dx }  \right)  }^{ 2 }.$$
I tried it by first finding $\dfrac { dy }{ dx } $ using quadratic formula but I am getting a complex differential equation
$\dfrac { dy }{ dx } =\dfrac { -{ x }^{ 3 }\pm \sqrt { { { x }^{ 6 }+ }4{ x }^{ 2 }{ y }^{ 2 } }  }{ 2y } $

Hint: Since $y\equiv0$ is a solution, we can as well multiply the equation by $y$. Then, with $$z=\frac12y^2+\frac18x^4,$$ we arrive at $$2x^2z=z'^2,$$ after an elementary calculation.
Can you take it from there?
