Find the general solution to the homogeneous differential equation $$\frac{d^2y}{dt^2} + 12\frac{dy}{dt} + 36y = 0$$
The solution can be written in the form $$y = C_1 f_1(t) + C_2 f_2(t)$$ with $f_1(t) =$ and $f_2(t) =$ Left to your own devices, you will probably write down the correct answers, but in case you want to quibble, enter your answers so that the functions are normalized with $f_1(0)=1$ and $f_2(0)=0$.