Hi, I posted this on the homework forum, but I haven't gotten any responses there. I thought there might be a better chance here.(adsbygoogle = window.adsbygoogle || []).push({});

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

I have the ODE

h'' + h'/r + λ^{2}h = 1,

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

2. Relevant 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!

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# Solving a non-homogeneous ODE with Bessel functions?

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