(a) Let D = , and an, an-1,..., a1, ao E R. Is anx" D" + an-1x"-1Dn-1+ ... + a1xD+ ao a linear operator? Prove or provide a counterexample. dx (b) Find an operator A that annihlates the following...

Just C please

Extracted text: (a) Let D = , and an, an-1,..., a1, ao E R. Is anx" D" + an-1x"-1Dn-1+ ... + a1xD+ ao a linear operator? Prove or provide a counterexample. dx (b) Find an operator A that annihlates the following functions. i. In(x) ji. ta , α R iii. sin(3 In(x)) (c) Solve the following using the annihlator method. i. y" +3y' + 2y = 5 In(x) ii. x'y" + 7xy' + 10y = 4x? cos(3lIn(x)) + x-3