a)Use the table of Laplace transforms to find the transform of the followingfunction and state the region of convergence: f(t)=\left(t^{2}+4\right) e^{3 t} Find the inverse Laplace transform of the function: Use Laplace transform methods to find the solution to the 2nd order ordinary differential equation given below: \frac{d^{2} y}{d t^{2}}-3 \frac{d y}{d t}+2 y=e^{3 t} when the initial conditions are given as \text { when } t=0 \quad\left\{\begin{array}{c} y=0 \\ \frac{d y}{d t}=0 \end{array}\right.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8