4. (a) Solve x2y" - 3xy' + 4y = x2 log(x), x > 0. (b) Solve x2y" + 5xy' + 4y = 0. (c) y" + p(x)y' + Q(x)y =0 i. Do the function y1(x) = x and y2(x) = sin(x) be the solution of the above differential equation ? Please fully justify your answer. ii. Assume the following the lemma is right. Let f(x) E C2 on an closed and bounded interval I. If f(x) takes infinity many zeros over I, then we can find a ro E I such that f(x), f'(x) vanish at xo. Suppose y1(x) is a solution of the above given differential equation on a closed and bounded interval I. Use above lemma to check if y1(x) can take infinity many zeros in