Use (18) in Section 6.4. x²y" + xy' - (x²x² + ²y = 0 (18) Find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.) x²y" + xy' - (16x² + y = 0 O y(x) = C₁J4(9x/4) + C₂Y4(9x/4) y(x) = C₁J3/2(4x) + C₂³-3/2(4x) O y(x) = C₁J4(3x/2) + C₂Y4(3x/2) O y(x) = C₁13/2(4x) + C₂K3/2(4x) O y(x) = C₁J9/4(4x) + C₂³-9/4(4x)
Use (18) in Section 6.4. x²y" + xy' - (x²x² + ²y = 0 (18) Find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.) x²y" + xy' - (16x² + y = 0 O y(x) = C₁J4(9x/4) + C₂Y4(9x/4) y(x) = C₁J3/2(4x) + C₂³-3/2(4x) O y(x) = C₁J4(3x/2) + C₂Y4(3x/2) O y(x) = C₁13/2(4x) + C₂K3/2(4x) O y(x) = C₁J9/4(4x) + C₂³-9/4(4x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use (18) in Section 6.4.
x²y" + xy' - (x²x² + v²)y=0 (18)
Find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.)
x²y" + xy' - (16x² + 2y = 0
O y(x) = C₁J4(9x/4) + C₂Y4(9x/4)
y(x) = C₁J3/2(4x) + C₂³-3/2(4x)
O y(x) = C₁J4(3x/2) + C₂Y4(3x/2)
O y(x) = C₁13/2(4x) + C₂K3/2(4x)
O y(x) = C₁J9/4(4x) + C₂-9/4(4x)
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