The equation is y"+8y'+25y=0 with y(0)= 2 & y'(0)=0

I calculated the general solution and figured out the motion is Underdamped. I can't seem to figure out the solution to the initial value problem.

I found S1 and S2 to be equal -4 +/- 3i ad the Ygen = (k1)^(-4t)cost(t) + i(k2)e^(-4t)sin(t)