In this exercise you will solve the initial value problem y" − 8y + 16y: e-4x 1+x²⁹ y(0) = 8, y'(0) = −1. (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 8y' + 16y = 0 is the function Yh(x) = C₁ Y₁ (x) + C₂ y₂(x) = C₁+C₂. NOTE: The order in which you enter the answers is important; that is, C₁ f(x) + C₂g(x) ‡ C₁g(x) + C₂ f(x). (2) The particular solution y(x) to the differential equation y" + 8y' + 16y= is of the form y(x) = y₁ (x) u₁(x) + y₂ (x) u₂(x) where u{(x) = and u₂(x) = e-4x 1+x² (3) The most general solution to the non-homogeneous differential equation y" — 8y + 16y= e-4x is 1+x² y = + dt+ 0 dt