MHB Initial Conditions in Laplace Transform of Second Order Differential Equations

[kJS]

And also:
y`+2y=2(1-e^-2t) Y(0)=0
y¨-2y`+y = t+e^t y(0)=1 and y`(0)=0

Please help me out here folks ;)

 

[Ackbach]

It's a bit unusual to have an initial condition in the frequency domain. Are you sure the initial condition for the first DE is $Y(0)=0$? Or is it $y(0)=0$? In any case, what do you get when you Laplace Transform the entire equation? (For each DE.)