Finding the singular points for this differential equation

[JKC]

Homework Statement

If d^2/dx^2 + ln(x)y = 0[/B]

Homework Equations

included in attempt

The Attempt at a Solution

I was confused as to whether I include the power series for ln(x) in the solution. It makes comparing coefficients very nasty though.

Whenever I expand for m=0 for the a₀ I end up with a pretty nasty expansion. Can somebody tell me where I'm going wrong here?

Thanks

Note: I understand how tedious this part of calculus is so thanks in advance to anyone willing to take the time to lend a hand.

 

[Mark44]

Homework Statement

If d^2/dx^2 + ln(x)y = 0[/B]

You're missing y on the left side.

Homework Equations

included in attempt

The Attempt at a Solution

I was confused as to whether I include the power series for ln(x) in the solution. It makes comparing coefficients very nasty though.

View attachment 213501

Whenever I expand for m=0 for the a₀ I end up with a pretty nasty expansion. Can somebody tell me where I'm going wrong here?

Thanks

Note: I understand how tedious this part of calculus is so thanks in advance to anyone willing to take the time to lend a hand.

I think you might be going about it wrong. Based on what you posted, the question is not asking you to solve the DE -- just find the singular points. Obviously you're not going to get a series in powers of x, because the DE is not defined at x = 0.