Solve the ODE x²y"(x)+ axy'(x) + (1+ b²x²) y(x) = 0, where a, b are real parameters, using the substitution y(x) = xv(x). Adjust n and a so that the ODE for v becomes Bessel's ODE for Jo. Find the general solution y(x) for this value of a.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
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12.1.17 Solve the ODE x²y"(x)+ axy'(x) + (1 + b²x²)y(x) = 0, where a, b
are real parameters, using the substitution y(x) = x¯"v(x). Adjust n
and a so that the ODE for v becomes Bessel's ODE for Jo. Find the
general solution y(x) for this value of a.
Transcribed Image Text:12.1.17 Solve the ODE x²y"(x)+ axy'(x) + (1 + b²x²)y(x) = 0, where a, b are real parameters, using the substitution y(x) = x¯"v(x). Adjust n and a so that the ODE for v becomes Bessel's ODE for Jo. Find the general solution y(x) for this value of a.
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