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Use (18) in Section 6.4. x²y" + xy' - (a²x² + 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 - (4x² + y = 0 16 Oy(x) = C₁³9/16(2x) + C₂-9/16(2x) Oy(x) = C₁₂(3x/4) + C₂Y₂(3x/4) O y(x) = C₁J3/4(2x) + C₂³-3/4(2x) O y(x) = C₁₂(9x/16) + C₂Y₂(9x/16) O y(x) = C₁13/4(2x) + C₂K 3/4(2x)

Use (18) in Section 6.4. x²y" + xy' - (a²x² + 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 - (4x² + y = 0 16 Oy(x) = C₁³9/16(2x) + C₂-9/16(2x) Oy(x) = C₁₂(3x/4) + C₂Y₂(3x/4) O y(x) = C₁J3/4(2x) + C₂³-3/4(2x) O y(x) = C₁₂(9x/16) + C₂Y₂(9x/16) O y(x) = C₁13/4(2x) + C₂K 3/4(2x)

Advanced Engineering Mathematics
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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Use (18) in Section 6.4. x²y" + xy' - (a²x² + 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 - (4x² + y = 0 16 Oy(x) = C₁³9/16(2x) + C₂-9/16(2x) Oy(x) = C₁₂(3x/4) + C₂Y₂(3x/4) O y(x) = C₁J3/4(2x) + C₂³-3/4(2x) O y(x) = C₁₂(9x/16) + C₂Y₂(9x/16) O y(x) = C₁13/4(2x) + C₂K 3/4(2x)
Transcribed Image Text:Use (18) in Section 6.4. x²y" + xy' - (a²x² + 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 - (4x² + y = 0 16 Oy(x) = C₁³9/16(2x) + C₂-9/16(2x) Oy(x) = C₁₂(3x/4) + C₂Y₂(3x/4) O y(x) = C₁J3/4(2x) + C₂³-3/4(2x) O y(x) = C₁₂(9x/16) + C₂Y₂(9x/16) O y(x) = C₁13/4(2x) + C₂K 3/4(2x)
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