# Is this ODE a well-known and studied one?

I came across this ordinary differential equation $$x \,(y')^2+a=0\,,$$ where $$a$$ is a real number, $$x$$ is a real variable and $$y$$ is a real algebraic function of $$x$$. I was wondering whether this is a well-known and studied ODE or not.

If you make the change of variable $$x = t^4$$, $$y(x) = u(t)$$, you find $$u$$ satisfies Chrystal's equation.
If $$a<0$$ and $$y(x):= 2 \sqrt{-a} \sqrt{x}$$, then $$y$$ is a solution of differential equation on $$(0, \infty).$$