Suppose that the characteristic equation for a differential equation is (r−2)2(r−3)2=0(r−2)2(r−3)2=0. (a) find such a differential equation, assuming it is homogeneous and has constant coefficients. enter your answer using y, y′,y′′,y′′′,yy, y′,y′′,y′′′,y for the dependent variable and its derivatives. (b) find the general solution to this differential equation. in your answer, use c1,c2,c3c1,c2,c3 and c4c4 to denote arbitrary constants, use yy for the dependent variable, and use xx for the independent variable. enter c1c1 as c1, c2c2 as c2, etc.