Final Practice T1 Q13 - Looking for a detailed worked solution with theoretical explanation

This question has several parts. Please scroll down and try to answer all sub-questions until you get to "END OF THIS QUESTION". For the questions below, you will need to use Maple syntax for expressions with variables c or y. We show some expressions in , be careful to use the right variable in the right context. Expression How to enter x 24x2 - VI-2x x^ (-2) + x^2 + sqrt ( 1 - 2* x) / (4+5*x*3) 4+523 4e5x 4*exp (5*x) Inx = logx = loge X In (x) sin x, cost, tan , sect, cscosin (x) , cos (x) , tan (x) , sec (x) , csc (x) sin x, cos x, tan la arcsin (x) , arccos (x), arctan (x) Note: the parentheses ( ) must be present in the evaluation of functions, even if just evaluating at c. For instance, it is sin (x) , not sin x. Note that you must enter exact answers, for example, for 1/3 do not enter a decimal approximation such as 0.3333333333. For negative denominators you must use brackets, for example, -3/2 or 3/ (-2) but not 3/-2. Enter pi and exp (1) for 7 and the Euler number e. Consider the vibrating system modelled by the equation y"tay + 6y= -13 sinc. (a) Find the smallest positive value of a such that the solution to the homogeneous equation does not oscillate. a (b) Fix now a = 12. Evaluate the non-decaying part of the solution of the above inhomogeneous differential equation. (A function y () is non-decaying if y () does not tend to the 0 function as I -+ 00 ). y (x) = END OF THIS