Consider the following integral equation, $so$ called because the unknown dependent variable, $y,$ appears within $an$

integral:

${\displaystyle \underset{0}{\overset{t}{}}}sin(4(t-w))y(w)dw=4t^2$

This equation $is$ defined for $t0.$

$a.$ Use convolution and Laplace transforms $to$ find the Laplace transform $of$ the solution.

$Y(s)=L\{y(t)\}=$

$b.$ Obtain the solution $y(t).$

$y(t)=$