In this exercise you will solve the initial value problem y′′−8y′+16y=e−4x1+x2, y(0)=6, 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 e^(4x) +c2 xe^(4x) . 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 yp(x) to the differential equation y′′+8y′+16y=e−4x1+x2 is of the form yp(x)=y1(x) u1(x)+y2(x) u2(x) where u′1(x)= and u′2(x)= . (3) the most general solution to the non-homogeneous differential equation y′′−8y′+16y=e−4x1+x2 is