Problem $3.(12$ pts$)$

$T^{\text{'}\text{'}}(t)-3T^{\text{'}}(t)+2T(t)=f(t).T^{\text{'}}(0)=T(0)=0.$ Given $f(t)$ defined as a distribution function as follows:

$f(t)=\{\begin{array}{cc}0,& t2\\ 3,& 24\end{array}$

Sketch the function $(t)$

Solve the ODE using LAPLACE TRANSFORM.