Exercise 2 (25 points) (L02 and L03, 30 minutes) Consider the following second order differential equation: 1) a) Find the general solution of the homogeneous equation. b) Without calculating the particular solution yp(x), give its general form using the undetermined coefficients method. c) Prove that IP(z) =ã4e_3x d) Deduce the solution of the equation (E), if y(0) = 1 and y'(0) = 1. 2) Using Laplace transforms, re-find the solution of (E) with the same initial conditions yf0) 1 and (0)1
Show transcribed image text Exercise 2 (25 points) (L02 and L03, 30 minutes) Consider the following second order differential equation: 1) a) Find the general solution of the homogeneous equation. b) Without calculating the particular solution yp(x), give its general form using the undetermined coefficients method. c) Prove that IP(z) =ã4e_3x d) Deduce the solution of the equation (E), if y(0) = 1 and y'(0) = 1. 2) Using Laplace transforms, re-find the solution of (E) with the same initial conditions yf0) 1 and (0)1