Solving y"+9y=H(t-1) with Laplace Transform

[Fibonacci]

Hi, just like to check my answer with someone for the this question

calculate y"+9y=H(t-1) y(0)=0 y'(0)=-2 using laplace method
H is heaviside fuction

my solution:

y=cos(3t)-2sin(3t)/3 + H(t-1)/9(H(t-1) + cos (3t-3) )

thanks

 

[matematikawan]

y(0)=1 for your solution. Not consistent with the given initial value.