Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why?
f = fH + fP where fH is the homogeneous solution and fP is the particular solution.
The Attempt at a Solution
So I've solved this equation to get: f(t) = C1e4t + C2e-3t which I have checked is right.
My question is how may free parameters enter the solution? I'm not sure what this means - is it asking how many constants there are and the answer would therefore be 2? But I don't know why.
Please help! Thank you.