Solved: (Approximation) Show that for small Ixl we have 10
Chapter 5, Problem 5.1.83(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.)
\(36 x^{2} y^{\prime \prime}+18 x y^{\prime}+\sqrt{x} y=0\)
\(\left(y=x^{1 / 4} u, \frac{2}{3} x^{1 / 4}=z\right.\))
Text Transcription:
J_nu
J_- nu
36x^2 y “ + 18xy ‘ + sqrt{x} y = 0
(y = x^{1/4} u, 2 / 3 x^{1/4} = z)
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