PLEplesaplease answer these

(1 point) Suppose that a fourth order differential equation has a solution y = 2e3xx sin(x). (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. [:] help (equations) Note: for part (a), use primes to denote derivatives. (b) Find the general solution to this differential equation. In your answer, use A, B, C and D to denote arbitrary constants and x the independent variable. [y = e3x(A cos(x) + B sin(x)) + xe3x(Ccos(x) + B sin(x)) Note: for this part, you MUST enter y = before your answer. For example, if I thought the answer was y = Ae" + 3x2 I would literally enter y = Ae" + sz. (1 point) 3 -2 -2 The matrix A = 2 1 0 0 2 5 has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. eigenvalue = 0 multiplicity = dimension of the eigenspace = Is the matrix A defective? (Type "yes" or "no") yes