Being a physicist, I rarely encountered a nonlinear ODE. Accordingly, I have no idea how to solve the following equation:

y(x) * y''(x) + y'(x)^2 = 0

with y(0) = C, y'(x) = 0.

It's fairly obvious that one of the solutions is y(x) = C. But, how to find the other solution? I don't even know enough about general ODE to know is there another solution being the equation is not linear?

Thanks

*** I now see I should've posted this under the Differential Equations. Sorry! ***