I'm struggling really hard with this question, but especially with part a. If someone could please help me out with part A that would be amazing

PROBLEM 2: String vibrations with a body force In class, we showed that the displacement 71(32, t) of a nonuniform string satises 821; 82a _ :11 03172 PG 81:2 + Q, (2) where Q represents the vertical component of the body force per unit length. Here, we assume that Q is of the form Q = an. (a) Show that if a D the body force tends to push the string further away from its unperturbed position it = 0. (b) Apply separation of variables in the form u($,t) = ($)h(t) in the general case where po(:r) and abs) are functions of 3:, but To is a constant. Obtain ODEs for q5(:r) and Mt). (c) Solve the time-dependent problem for Mt). (d) Now assume that p and or are constant, with or