Find the infinite series solution about x = 0 for the following
differential equation x2y"+ 4xy' + (2+x)y = 0,without using k
substitution and using Bessel's, Legrende's, or frobenius
equations.
x2 y" + (x2+x) y’
+(2x-1) y = 0,
Find the general solution of y1 with
r1 and calculate the coefficient up to
c4 and also find the general expression of the
recursion formula, (recursion formula for
y1)
Find the general solution of y2 based on
theorem 4.3.1. (Hint, set d2 = 0)
Consider the second-order differential equation
x2y′′+(x2+ax)y′−axy=0 where a=−2 Is x0=0 a singular or ordinary
point of the equation? If it is singular, is it regular or
irregular? Find two linearly independent power series solutions of
the differential equation. For each solution, you can restrict it
to the first four terms of the expansion