help with 2nd order linear ODE

Hi, I'm a little unfamiliar with modelling, and having trouble understanding this one in particular about the dampled oscillating system, turned on at time t = 1:

y" + 5y" + 6y = 0 if 0<=t<=1

AND

= 6t - 6 if t>1

Q: what is the displacement y=y(t) during the time interval 0<= t <=1; and evaluate y(1) and y'(1) to two decimal places.

From what I've read, displacement is found by integrating and finding y (?) but I don't quite know how.. Any help or clues would really be appreciated.

Thanks(Nod)

Edit: I know how to get the characteristic roots (-2, -3) and general solution (y = yh = c1e^(-3x) + c2e^(-2x)), but how can i use these to find the displacement?