Linear Second Order ODE/y'' + 4 y = 8 x^2 - 4 x

Theorem
The second order ODE:
 * $(1): \quad y'' + 4 y = 8 x^2 - 4 x$

has the general solution:
 * $y = C_1 \sin 2 x + C_2 \cos 2 x - 1 - x + 2 x^2$