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## Homework Statement

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?

## Homework Equations

f = f

_{H}+ f

_{P}where f

_{H}is the homogeneous solution and f

_{P}is the particular solution.

## The Attempt at a Solution

So I've solved this equation to get: f(t) = C

_{1}e

^{4t}+ C

_{2}e

^{-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.