(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is:

(x2 - 4) y′′ + 3xy′ + y = 0, y(0) = 4, y′(0) = 1

2. Relevant equations

Existence of power series:

y = [tex]\sum c(x-x0)^n[/tex]

or

y = (x-x0)^r[tex]\sum c(x-x0)^n[/tex]

3. The attempt at a solution

I know the point x=2 is an ordinary point of the differential equation, since:

(x^2 - 4) y′′ + 3xy′ + y = 0

y′′ + 3xy′/(x^2-4) + y/(x^2-4)=0

P(x) = 3x/(x^2-4) Q(x) = 1/(x^2 - 4)

x can't equal to +-2.

But then the thing is that, our teacher has only given us problems where 0 is the regular singular point, but it seems like in this problem has x=+-2 as the regular singular points. Would that mean that there exists two li solutions in a form of a power series where:

y = (x-2)^r[tex]\sum c(x-2)^n[/tex]

y = (x+2)^r[tex]\sum d(x+2)^n[/tex]

(c and d being constants)

Then each one would have a different set of indicial roots which would give two separate r values in which there would be two different series for each y?

Or should I not be doing the method of Frobenius?

I already tried setting up the sum using the method of frobenius using only x=2 as the ordinary point (because I assumed I should only use the positive term), but for the indicial equation, I obtained two indicial roots of r=0,0, which left me thinking maybe I'm doing this completely wrong and don't know what I'm doing. :( This is probably the most confusing part of this class... Can anyone give me some guidance on what I should do? :(

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Solving differential equation using power series representation

**Physics Forums | Science Articles, Homework Help, Discussion**