the equation is given, $\displaystyle x'' + 4x' + 4x = f(t)$

where f(t) = { t , 0 < t < 2 ; 0 , 2 < t }

I am having trouble getting the laplace of the $\displaystyle f(t)$ function.

I believe you would getL{f(t)}==L {[1 - H(t-2)]t}

Which would beL{t}-L{t*H( t-2 )}

Which I think would be $\displaystyle 1/u^2 - (e^-2u)/u^2$

Which Is$\displaystyle (1-e^-2u)/u^2$, but this is incorrect.

The solution is $\displaystyle 1/u^2 - (e^-2u)[2/s +1/u^2]$

is there anyone that could help me? Thank you in advance