(c) (3 marks) Compute the derivative of g(x) = (1 - x)es (2). (d) (3 marks) Conclude that f(x) is a solution of the differential equation f'(x) = ef(x). Q4: Consider the differential equation ( * ) f" (2) + 2f (2) + f (2) - 0 with initial conditions f(0) = 0 and f'(0) = 1. (a) (2 marks) Suppose the solution is given by the power series f(x) = ) ann. Rewrite ries f( 2 ) - n=0 the equation (*) as a power series expression. (b) (2 marks) Find the values of the coefficients do and a1. (c) (4 marks) Find a recursive formula for an, n 2 2, in terms of an-1 and an-2. (d) (4 marks) Use induction to show that an+1 = ( -1)n