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First use (20) in Section 6.4. 2a y" +1-28 y² + (6²c²x²c-2 + a²-p²2²)y = 0, y' X Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27) 2 TX y(x) = J1/2(x) = 2 π.χ = sin(x) (26) J-1/2(x) to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.) 4x²y" - 4xy' + (64x² + 3)y = 0 = 0, p≥0 (20) cos(x) (27)

First use (20) in Section 6.4. 2a y" +1-28 y² + (6²c²x²c-2 + a²-p²2²)y = 0, y' X Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27) 2 TX y(x) = J1/2(x) = 2 π.χ = sin(x) (26) J-1/2(x) to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.) 4x²y" - 4xy' + (64x² + 3)y = 0 = 0, p≥0 (20) cos(x) (27)

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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First use (20) in Section 6.4. y" + 1 - 2a y(x) = X J1/2(x) -y' + (b²c²x2²c- Need Help? - 2 Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27) 2 π.χ 2 cos(x) V TEX + Read It sin(x) (26) J-1/2(x) to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.) 4x²y" - 4xy' + (64x² + 3) = 0 a²-p²2²)y= -p-c (27) = 0, p≥ 0 Watch It (20)
Transcribed Image Text:First use (20) in Section 6.4. y" + 1 - 2a y(x) = X J1/2(x) -y' + (b²c²x2²c- Need Help? - 2 Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27) 2 π.χ 2 cos(x) V TEX + Read It sin(x) (26) J-1/2(x) to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.) 4x²y" - 4xy' + (64x² + 3) = 0 a²-p²2²)y= -p-c (27) = 0, p≥ 0 Watch It (20)
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