1. Consider the general linear second-order ODE Poy" +P1y + P2y = - (1) where po, P1, and p2 are functions of x and A is a constant parameter. The standard form of the Sturm-Liouville ODE (py')' + qy=-Xwy, where p, q, and w are functions of x and A is a constant parameter. (a) Assuming that po, P1, P2, and à are given, multiply Eq. 1 by w. By comparing to Eq. 2, show that the unknown p, q, w, A must satisfy p = wpo, p' = wp1, q = wp2, and λ = A. (b) Show that p = = exp(fdx). (c) Show that w = = -Ay, PO exp(dx). der ODF can in principle he put into the

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