(a) Show that the Bessel function J0(x) given by Formula(4) of Section 9.8 satisfies the
Chapter 9, Problem 45(choose chapter or problem)
Show that the Bessel function \(J_{0}(x)\) given by Formula (4) of Section satisfies the differential equation \(x y^{\prime \prime}+y^{\prime}+x y=0\). (This is called the Bessel equation of order zero.)
(b) Show that the Bessel function \(J_{1}(x)\) given by Formula (5) of Section satisfies the differential equation \(x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0\). (This is called the Bessel equation of order one.)
(c) Show that \(J_{0}^{\prime}(x)=J_{1}(x)\).
Equation Transcription:
Text Transcription:
J_0(x)
xy”+y’+xy=0
J_1(x)
x^2y”+xy’+(x^2-1)y=0
J_0(x)=-J_1(x)
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