We are covering Laplace Transforms, and Heaviside Functions.

In case it is difficult to read.. the { symbol is indicating a piecewise function.

We were given the take home problem:

y''(t) + y(t) = { t/2 0 <= t < 6

{ 3 t > 6

y(0) = 0

y'(0) = 1

I am trying to transition this to the heaviside "style" like our teacher did in class, so far I have..

step 1:

f(t) = t/2 + { 0 0 <= t < 6

{ 3 - t/2 t > 6

step 2:

t/2 + U6(t) * (3 - t/2) { 0 0 <= t < 6

{ 1 t > 6

I'm not entirely sure if I did this correctly. And, if it is correct, I'm not sure what the next step would be.

I know this is a lot of information, thank you for your help.