Find the general solution to the homogeneous differential equation $$\frac{d^2y}{dt^2} - 6\frac{dy}{dt} + 45y = 0$$
The solution has 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 their values at $t = 0$ equal to 0 and 1(respectively), and they are expressed as simply as possible.