Use the Laplace transform to solve the initial value problem

$y^{\text{'}\text{'}}-7y^{\text{'}}12y=f(t),y(0)=0,y^{\text{'}}(0)=0$

where

$f(t)=\{\begin{array}{ccc}0& if& 0t<mn>4</mn>\\ -12t& 51if& t4\end{array}$

Note: Use $u$ for the step function.

$y(t)=$

$$