5. Denote the first 7 digits of your student number as 81828384858687. Use the Laplace Trans- form to solve the following initial valued problem: ď² f(t) dt² df (t) 2 +

(10 +82 +83 +84) f(t) dt = u(t) where f(0) = 2 + 85 and f'(0) = 4 + 86, where u(t) denotes the unit step function. Show the values of $1828384858687 at the beginning of the answer. Show your working. [15 marks]