5-1(10 marks)(6) A s">

(a) By applying the definition of Laplace Transform, solve the Laplace transform of f(t)= -2 Ost<5 t> 5 -1 (10 marks) (6) A second-order differential equation is given as follows: f"(t)-9f(t) = g(t) where g(t) is a non-continuous function represented by, g(t) = 5H(t)+H(t-1). Solve the differential equation using Laplace Transform by applying partial fraction and second shift theorem for inverse Laplace Transform, if the initial conditions are f(0) = 0 and f'(o)=1. (20 marks)