How to solve these two questions of calculus? 1.

Consider the second-order ordinary differential equation d2y dy E+aE+Qy0, where a is a positive real number. a) For which value(s) of a does the differential equation have general solution y = AeAlm + BeA2m, for some A1,)\\2 E R, with A1 75 A2? Enter your answer in the box below. :llh (Your answer should be an interval) b) Assuming the general solution to be as in part (a), find the value of a such that A1 = 2 and write your answer in the box below. What is A2 in this case? >4 [\\3 H L... E c) Let now a = 6 and consider the non-homogeneous differential equation dzy dy 3m E+6E+9yme . Find one particular solution and enter your result in the box below using Maple syntax (notice that you don't have to include the general solution). 2W) = :i a Consider the differential equation dy 4 4 a) It is given that if both sides of the differential equation are multiplied by a function (a:) , the differential equation will become %((m)y) = rm (3m + 2) e495 . Find q5(m) and write your answer in the box below. W) = S E b) Setting the initial condition y(1) = 0,what is the largest domain I for the solution y? I=Sm