PLEASE ONLY DO ALL PARTS OF C (i-iv)

(2) Let's consider the Euler equation z'y" - 3.xy' - 5y = f(x) on the interval (0,00) for various "forcing functions" f(x). (a) First solve the complementary equation, that is when f(x) = 0. Put the answer in the box provided. (b) Now suppose f(x) = r". Find a particular solution of the form yp = Ax. Then construct the general solution. Put the answer in the box provided. 1 (c) Now suppose f(x) = (i) Explain why attempting to find a particular solution of the form yp = is futile. (ii) Try Reduction of Order (have y = uy, where y is a non-trivial comple- mentary solution) to construct the general solution. Put the answer in the box provided (iii) Now try Variation of Parameters to find a particular solution to the equa- tion (yp = uyi + vya where y: y2 form a basis of solutions to the comple- mentary equation). Then construct the general solution. Put the answer in the box provided. You are encouraged to use the standard formulas involving the Wron- skian) for u' and v'. y = (iv) Which did you like better? Can you imagine situations where one can be used, but not the other, and vice versa