Second Order ODE/y y'' + (y')^2 = 0

Theorem
The second order ODE:
 * $(1): \quad y y'' + \paren {y'}^2 = 0$

has the general solution:
 * $y^2 = C_1 x + C_2$

Proof
Using Solution of Second Order Differential Equation with Missing Independent Variable, $(1)$ can be expressed as: