Show that the two linearly independent solutions of xy" – y + xy = 0, x > 0 can %3D be obtained as xJ1(x) and xY1(x) by making a suitable substitution of the dependent variable y. Here J1(x) and Y1(x) are, respectively, Bessel function of first kind and second kind of order 1.
Show that the two linearly independent solutions of xy" – y + xy = 0, x > 0 can %3D be obtained as xJ1(x) and xY1(x) by making a suitable substitution of the dependent variable y. Here J1(x) and Y1(x) are, respectively, Bessel function of first kind and second kind of order 1.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Do question number 3
Transcribed Image Text:2. Find the complete solution of the differential equation (D – a)°y = a", where a and b are
positive integers and D stands for the operator d/d.x.
3. Show that the two linearly independent solutions of xy" –- y + xy = 0,
x > 0 can
be obtained as xJ(x) and xY1(x) by making a suitable substitution of the dependent
variable y. Here J1(x) and Y1(x) are, respectively, Bessel function of first kind and second
kind of order 1.
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