(1 point) In this exercise you will solve the initial value problem y" - 6y' + 9y= e-3x 1+x2' y(0) -3, y(0) : (1) Let C₁land C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 6y' + 9y=0|is the function y (x) = C₁ y₁(x) + C2 y2(x) = C₁| +C₂l NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C2g(x) C₁g(x) + C₂f(x). (2) The particular solution y, (x) to the differential equation y" + 6y' +9y= where u₁ (x) =| and u(x) = 1+x² is of the form y, (x) = y₁ (x) u₁ (x) + y2 (x) u₂ (x) (3) The most general solution to the non-homogeneous differential equation y" - 6y' + 9y= e-3x is 1+x² y =| +1 dt + dt\