Problem 8. (12 points) Suppose that the characteristic equation for a differential equation is (r - 5)2(r - 4)2 = 0. (a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using y, y', y", y", y" for the dependent variable and its derivatives. help ( equations ) (b) Find the general solution to this differential equation. In your answer, use C1, C2, C3 and c4 to denote arbitrary constants, use y for the dependent variable, and use a for the independent variable. Enter c1 as c1, C2 as c2, etc. help ( equations )