In an integro-differential equation, the unknown dependent variable $y$ appears within an integral, and its derivative $dy/dt$ also appears. Consider the following initial value problem, defined for $t \geq 0$: $$\displaystyle\frac{dy}{dt} + 4 \int_0^t y(t-w)\, e^{-4 w} \ dw = 6, \quad \quad y(0) = 0.$$

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 $y(t)$.
   
   $y(t) =$