Problem $2$:

Find

$L[e^{2t}{t}^2]$

Problem $3$:

Find $L^{-1}{?}^{}[\frac{3s+6}{s^2+3s}].$

Problem $4$:

Solve the initial value problem using Laplace transform.

$y^{\text{'}\text{'}}-4y^{\text{'}}+9y=t,y(0)=0,y^{\text{'}}(0)=1$