In this problem you will use variation of parameters to solve the nonhomogeneous equation $$y''+4y'+4y = -4e^{-2t}$$

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A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)

$\quad$

B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian.

$\quad \phantom{\mathrm{W}(y_1,\,)} y_1 =$

$\qquad y_2 =$

$\quad \mathrm{W}\bigl(y_1, y_2\bigr) =$

C. Compute the following integrals. (In the differential equation, $g(t) = -4e^{-2t}$ is the "forcing function".)

$\quad \displaystyle \int \frac{y_1 g}{W} dt =$

$\quad \displaystyle \int \frac{y_2 g}{W} dt =$

D. Write the general solution. (Use c1 and c2 for $c_1$ and $c_2$).

$\quad y =$

(Note: Your general solution will only be correct if it is a general solution to the differential equation.)