This is a second order nonlinear differential equation. By rearranging the terms, we can write it in a form that is easier to work with:

yy'' = (y')^2

y'' = (y')^2 / y

Let u = y',

Then y'' = du/dx = d(u)/dx

So the equation becomes:

du/dx = (u)^2 / y

Separating variables, we have:

y dy = u du

Integrating both sides, we get:

1/2 y^2 = 1/2 u^2 + C

Where C is the constant of integration.

Therefore, the general solution to the differential equation yy'' = (y')^2 is given by:

y^2 = u^2 + C

or

y^2 = (dy/dx)^2 + C