1. 10pts. Using Laplace transforms, solve the following ODE initial value problem for the function $x(t)$. Although you can use a program to calculate the partial fraction decomposition, make sure to show what the decomposition is, and how you're applying the Laplace/inverse Laplace transform.
$\ddot{x}(t) - 8\dot{x}(t) + 12x = e^{3t}$, $x(0) = 0$, $\dot{x}(0) = 4$
2. 5pts. Rewrite the second order ODE above as a first order ODE of two variables.