Question 1 (4+4+4=12 marks) Consider the following second order differential equation y" - 4y + 8y = f(x) 1. Find the solution of the equation when f(x) = 0. 2. Find the form of a particular solution when f(x)= x² + cosx- re² sin 2x. 1 3. Find a particular solution when f(x) = sin 2x Question 2 (14 marks) Find the recurrence Formula and the 6 first terms of the power series solution about zo = 0 of the initial value problem [(x²-1)" - xy + xy=0 [y(0) = 2, '(0) = 1. Question 3 (8+6=14 marks) Consider the system X'(t) = AX(t) with A = - (²44) 1. Find the eigenvalues and the eigenvectors of the matrix A. 2. Find a fundamental set of real valued solutions of the system.