In class we discussed the hybrid approach to the solution of a singular problem. We arrived to the following problem F + Fo+FoFo = 0, Fo(o) = 1, which is subject to the matching condition as p~ 0: Fo~a/p. Defining x(a) = lim (Foa ln p), we closed the problem by the equation x(a) = -alne. Our goal is the determinate of a for a given e. We want to formulate a better problem, where we avoid the singular behavior of Fo at small p. We started in class by deriving a refined local approximation for Fo near p = 0, valid up to ord(p). 1. Define a function F(p) which avoids the singular a ln p behavior of Fo at small p. Use this opportunity to make F(p) vanish at o. 2. Write a code for solving the problem governing F(p) for a given a. 3. Write a code for the determination of a for a given e. Obtain a fore = 0.01.