4. Find the solution and final value (when t→ 0) of the following differential equation by using Laplace transform. Include the mathematical method to justify your solution and state any

properties of Laplace Transforms that you have used to perform your manipulations. (12) \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+c x=2 e^{-4 t} \text { Where } \frac{d x}{d t}=1 \text { and } x=0 \text { when } t=0 b=3 \text { and } c=3