y'' + 2y' -35y = T(t)

Where T(t) =

1 from 0 to 1

0 from 1 to infinity

y'(0) = 0, y(0) = 0

part 1:

Y(s) = ?

After taking Laplace of both side I get

(s^2-2s-35)Y(s) = 1/s

Y(s) = (1/s)(1/(s^2-2s-35))

but it's wrong...

and second part

Find the inverse transform to find y(t)

How would I approach that?

Thank you!!!