Suppose that the characteristic equation for a differential equation is (r−3)2(r−5)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. equation editorequation (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 x for the independent variable. enter c1 as c1, c2 as c2, etc.