An equation encountered in a boundary-value problem is (x^2-9)y'' + 2xy' - 6y = 0.
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Ordinary differential equations
Conditions of Validity, Ch Series solutions, singular points and where the special functions come from
Problem
An equation encountered in a boundary-value problem is (x2−9)y′′+2xy′−6y=0.
((a)) Classify the points x=3 and x=−3 (ordinary, regular singular, or irregular singular), showing the limits you use.
((b)) A series solution is sought about the ordinary point x=0. Using only the location of the singular points of the coefficients, predict the radius R within which every series solution about x=0 is guaranteed to converge (do not construct the series).