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 get L{f(t)} == L { [1 - H(t-2)]t }
Which would be L{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