In this exercise you will solve the initial value problem e-4z y" – 8y + 16y = 1+ x² y(0) = –1, y(0) = –2. %3D (1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" – 8y' + 16y = 0 is the function Yn(x) = C1 y1(x) + C2 y2(x) = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(x)+ C29(x) 7 C19(x) + C2f(x). (2) The particular solution yp(x) to the differential equation y" + 8y' + 16y = is of the form 1+r? Yp(x) = Y1(x) u1(x) + Y2(x) u2(x)where u (x) = and u (x) = (3) The most general solution to the non-homogeneous differential equation y" – 8y + 16y = is 1+z
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