Consider the following linear homogeneous differential equations with initial conditions: y" - 2sy = 0 y(0) = 1, y'(0) = 0 y" + y' - 2y = 0 y(0) = 1, y'(0) = 0 y" + 2y' + y = 0 y(0) = 0, y'(0) = 1 y" - 9y = 0 y(0) = 1. y'(0) = 0 y" + y' = 0 y(0) = 2, y'(0) = -1 y" + 4y = 0 y(0) = 1, y'(0) = -1 y" - 4y' + 13y = 0 y(0) = 1, y'(0) = 0 for each of the equations given, find the characteristic equation and solve the differential equation to find the solution