Exercise 104

Solve $x_1'' = -3x_1 + x_2 + t$, $x_2'' = 9x_1 + 5x_2 +\cos(t)$ with initial conditions $x_1(0) = 0$, $x_2(0) = 0$, $x_1'(0) = 0$, $x_2'(0) = 0$ using eigenvector decomposition.