Consider the following initial value problem, defined for $t0$ :

$x^{\text{'}}-6x={\displaystyle \underset{0}{\overset{t}{}}}(t-w)e^{6w}dw,x(0)=-3$

Find the Laplace transform of the solution.

$x(s)=L\{x(t)\}=$ help $(formulas).$

Obtain the solution $x(t).$

$x(t)=$

help $($formulas$)$

$$

Book: Section $6\mathrm{.}3$ of Notes on Diffy Qs