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Match the following guess solutions $y_p$ for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below.

A. $\displaystyle y_p(x) = Ax^2+Bx+C$ , B. $\displaystyle y_p(x) = Ae^{2 x}$ , C. $\displaystyle y_p(x) = A \cos 2 x + B \sin 2 x$ ,
D. $\displaystyle y_p(x) = (Ax + B)\cos 2 x + (Cx+D)\sin 2 x$ E. $\displaystyle y_p(x) = A x e^{2 x},$ and F. $\displaystyle y_p(x) = e^{3x}(A \cos 2 x + B \sin 2 x)$

1. $\displaystyle \frac{d^2y}{dx^2}+4y=x-\frac{x^2}{20}$

2. $\displaystyle \frac{d^2y}{dx^2}+6 \frac{dy}{dx}+8y=e^{2x}$

3. $\displaystyle y''+4y'+13y = 3 \cos 2x$

4. $\displaystyle y''-2y'-15y = e^{3x}\cos 2x$

In order to get credit for this problem all answers must be correct.