Consider the following integral equation, so called because the unknown dependent variable, $y$, appears within an integral: $$\int_0^t \sin(3 (t-w))\, y(w) \ dw = 6 t^2.$$ This equation is defined for $t \geq 0$.

1. Use convolution and Laplace transforms to find the Laplace transform of the solution.
   
   $\displaystyle Y(s) = {\mathcal L}\left\lbrace y(t) \right\rbrace =$
   
   
2. Obtain the solution $y(t)$.
   
   $y(t) =$