- #1

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1. Homework Statement

I have the ODE

h'' + h'/r + λ

^{2}h = 1,

where h = h(r), and I want to find h(r).

2. Homework Equations

The corresponding homogeneous equation is a Bessel equation that has the solution

h

_{h}= c

_{1}J

_{0}(λr) + c

_{2}Y

_{0}(λr),

where J

_{0}and Y

_{0}are Bessel functions.

Now I was planning on using h(r) = h

_{h}+ h

_{p},

where h

_{p}is a particular solution of the ODE.

3. The Attempt at a Solution

To find h

_{p}, I tried using variation of parameters, but I get to a point where I need to both differentiate and integrate a Bessel function, which turns out to be pretty hard. I'm wondering if I'm going in the wrong direction, or if my logic here is even valid.

Thanks!