(1 point) The IVP 4 3 (o)t e S 48 = in dp* dp* p? +1dp () s(2) = 877 SN dp '-2 #ap dp? ' -2 - 3 as) _ . dp ' -2 has a unique solution defined on the interval (1 point) Suppose that the characteristic equation for a differential equation is (r4)%(r 2)2 =0. (@) 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. (For the last one write y''"', with 4 primes.) help (equations) (b) Find the general solution to this differential equation. In your answer, use , , c3 and 4 to denote arbitrary constants, use y for the dependent variable, and use x for the independent variable. Enter ; as c1, y as c2, etc. (1 point) The general solution to the second-order day differential equation 4 dy + gy = 0 is in dac 2 dx the form y(a) = eat (c1 cos Bac + C2 sin Bac) . Find the values of a and B, where B > 0. Answer: a = and B = (1 point) For what values of r does the function y = 4ex satisfy the differential equation y" + 8y' + 7y = 0? The smaller one is The larger one (possibly the same) is