Given the initial value problem

$2y^{\text{'}\text{'}}+3y^{\text{'}}+y=f(t)=\{\begin{array}{ccc}0& if& t<mn>2</mn>\end{array}$

$tift2$

$y(0)=y^{\text{'}}(0)=0$

Which of the following is true?

L$$tfen birini se$$in:

A$.y(t)=1+2t+e^{-t}-2e^{-\frac{1}{2}t},t2$

B$.L\{y(t)\}=\frac{1}{s^2(s+1)}{e}^{-2s}$

C$.L\{y(t)\}=(\frac{1}{s}+\frac{2}{s^2}-\frac{1}{s+1}-\frac{2}{2s+1})e^{-2s}$

D$.$ None of these

E$.L\{f(t)\}=\frac{1}{s^2}{e}^{-2s}$