Solution: Use the powerful formulas (24) to do Probs. 21-28.
Chapter 5, Problem 5.1.105(choose chapter or problem)
Using the indicated substitutions, find a general solution in terms of \(J_{\nu}\) and \(J_{-\nu}\) or indicate when this is not possible. (This is just a sample of various ODEs reducible to Bessel's equation. Some more follow in the next problem set. Show the details of your work.)
\(x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-\frac{1}{16}\right) y=0\)
Text Transcription:
J_nu
J_- nu
x^2 y “ + xy ‘ + (x^2 - 1 / 16) y = 0
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