Solve using Laplace
= 1/6 + 1/3 e^-t – ½ e^-2t cos √2t- √2/3 e^-2t sen √2T
Also consider y'(0)=0
Tip, this is the solution:
= 1/6 + 1/3 e^-t – ½ e^-2t cos √2t- √2/3 e^-2t sen √2T