Second Order Equations-Constant Coefficient Homogeneous Complex: Problem 4 (4 points) For this problem, you do not need to get the coefficient of y" Ly be 1. (a) Find the general solution to y" + 9y = 0. In your answer, use A and B to denote arbitrary constants and t the independent variable. (b) Find the particular solution that satisfies y (0 ) = -4 and y'(0) = -21.Second Order Equations-Constant Coefficient Homogeneous Complex: Problem 2 (3 points) y" + 14y' + 53y = 0 (a) Give the characteristic polynomial for the differential equation. (use ?' as your variable.) (b) List the roots of the characteristic polynomial for the differential equation. (Complex numbers are okay in this answer.) (c) List the basic solutions for the differential equation, i.e. y1 (t). y/2(t ). (use t as the independent variable, and do NOT use complex numbers for this part.)Second Order Equations-Constant Coefficient Homogeneous Complex: Problem 1 (3 points) y" - 16y' + 89y = 0 (a) Give the characteristic polynomial for the differential equation. (use ?' as your variable.) (b) List the roots of the characteristic polynomial for the differential equation. (Complex numbers are okay in this answer.) (c) List the basic solutions for the differential equation, i.e. y1 (t ). y/2(t ). (use { as the independent variable, and do NOT use complex numbers for this part.)