In this problem you will solve the non-homogeneous differential equation y" +15y' + 50y = sin( sin(ex) (1) Let C1 and C be arbitrary constants. The general solution to the related homogeneous differential equation y" + 15y' + 50y = 0 is the function y(x) = C Y1(x) + C2 Y2(x) = C +C2 NOTE: The order in which you enter the answers is important; that is, Cf(x) + C29(x) + C19(x) + C2f(x). (2) The particular solution y (x) to the differential equation y + 15y' + 50y = sin(e5x) is of the form y(x) = Y1(x) u(x) + y2(x) u2(x) where u(x) = and u2(x) = = (3) It follows that u1(x) = and u2(x) = ; thus yp(x) = (4) The most general solution to the non-homogeneous differential equation y" + 15y' + 50y y = C +C+. = sin(e5x) is