there are 2 questions,For each one

Write a statement identifying which weekly course topic(s) or objective(s) are related to the exercise, or identify the "bigger picture" behind the exercise.

1. Construct an example of an nonhomogeneous ODE that cannot be solved using method of undetermined coeicients/annihlators but can be solved using variation of parameters. Explain why and then solve. 4. (a) Let D = , and an, an-1, ..., a1, do ER. Is and" D" + an-12" D"- + ... + axD + a a linear operator? Prove or provide a counterexample. (b) Find an operator A that annihlates the following functions. i. In(a) ii. to, a ER iii. sin(3 In(x)) (c) Solve the following using the annihlator method. i. y" + 3y' + 2y =51n(x) 72," + 7ry' + 104 = 1r2 cos(3 In y -3