1 solution of a linear differential equation has two parts homogeneous

Question

1. Solution of a linear differential equation has two parts: homogeneous solution and the particular solution. Homogeneous part has the 'pole terms', while the particular solution depends on the input function u(t).Consider a differential equation: ÿ + 5ý + 6y = u(t) а.What are the poles of this differential equation? b. Write the expression for the homogeneous part of the solution. c.Write the expression for the particular part of the solution if u(t) is a constant, u = 2. d. Write the expression for the particular part of the solution if u(t) is a sine function, u = 3 sin (3t +n/8). e. Write the expression for the particular part of the solution if u(t) is a polynomial, u = 3t + 2.