Solved: In each of 30 and 31, show that the point x = 0 is a regular singular point. In

QUESTION:

In each of 30 and 31, show that the point x = 0 is a regular singular point. In each problem try to find solutions of the form n=0 an xn. Show that (except for constant multiples) there is only one nonzero solution of this form in and that there are no nonzero solutions of this form in 31. Thus in neither case can the general solution be found in this manner. This is typical of equations with singular points. 2xy__ + 3y_ + xy = 0