- #1

DWill

- 70

- 0

## Homework Statement

Find the general solution of the given differential equation:

y'' + 9y = (t^2)(e^3t) + 6

## Homework Equations

## The Attempt at a Solution

I want to first find a particular solution using the method of undetermined coefficients, but I'm not sure what I should "guess" for the form of Y(t). I learned that if g(t) is some exponential function such as e^2t, then I should assume the form looks like Y(t) = Ae^2t, assuming no duplication with solution to the homogenous equation. This doesn't seem to be much harder, but the t^2 and the +6 is confusing me a bit. Any help for how I can get started? Thanks!