Final Practice T1 Q11 - 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 x or y. We show some expressions in , be careful to use the right variable in the right context. Expression How to enter x 2 +2 - V1-2x 4+523 x^ (-2) + x^2 + sqrt ( 1 - 2* x) / (4+5*x^3) 4e5x 4 *exp (5*x) In x = log x = loge T In (x) sin x, cost, tan , sect, csc Tsin (x) , cos (x) , tan (x) , sec (x) , csc(x) sin Ix, cos x, tana arcsin (x), arccos (x), arctan (x) Note: the parentheses ( ) must be present in the evaluation of functions, even if just evaluating at . 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. Enter exp (-3/2) for e-3/2 Consider the first order linear ODE (V22 - 16) y'tay= 12 - 16. We may find the general solution of this equation by finding the integrating factor first. (a) Let h (x) denote the integrating factor. Remember that this has the form h = ed 9. Type the expression of g in the box below. 9 (x) = (b) In order to find h, we need to make a substitution. From the list below, choose all substitutions that are recommended to try in this case 0 x=4tand O x = 4sin 0 O x= 4 cosh 0 O x = 4sec0 O x = 4 sinh 0 (c) Now find h (remember that we set the constant of integration equal to zero). We don't ask you to type the expression for h (), because the syntax can be complicated and it's easy to make errors. Instead, type in the box below only the value of h at x = v17, that is, h(v17) = END OF THIS