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Using Fourier Transform of derivatives and Table of Fourier Transform in the Appendix A, solve the following differential equation. y' + 9y = 8(x) (-∞ < x < ∞) y(0) = 0, y(∞) bounded. [Hint: F{8(x)} = V2n %3D

Using Fourier Transform of derivatives and Table of Fourier Transform in the Appendix A, solve the following differential equation. y' + 9y = 8(x) (-∞ < x < ∞) y(0) = 0, y(∞) bounded. [Hint: F{8(x)} = V2n %3D

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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Using Fourier Transform of derivatives and Table of Fourier Transform in the Appendix A, solve the following differential equation. y' + 9y = 8(x) (-∞ < x < ∞) 1 y(0) = 0, y(0) bounded. [Hint: F{8(x)} = %3D 2n
Transcribed Image Text:Using Fourier Transform of derivatives and Table of Fourier Transform in the Appendix A, solve the following differential equation. y' + 9y = 8(x) (-∞ < x < ∞) 1 y(0) = 0, y(0) bounded. [Hint: F{8(x)} = %3D 2n
f(x) f(w) = F(f) %3D Si if -b<x< b 1 2 sin bw lo otherwise S! ifb<x<c lo otherwise -ibo -iew iw V2n (a > 0) p- x² + a² V 2 if 0<x<b -1 + 2e®« – e-20 4 2x - b ifb <x < 2b otherwise ar if x>0 (a > 0) aherwise V2\a + iw) if b <x<c l0 aherwise la-nele - da-iub V2T(a – iw) retar if -b<x<b 7 2 sin b(w – a) lo otherwise if b<x<c bla-w - eila-w) 8 otherwise a - w (a > 0) sin ax 10 if |w| < a; Oif |w| > a (a> 0) 2. 3. 6.
Transcribed Image Text:f(x) f(w) = F(f) %3D Si if -b<x< b 1 2 sin bw lo otherwise S! ifb<x<c lo otherwise -ibo -iew iw V2n (a > 0) p- x² + a² V 2 if 0<x<b -1 + 2e®« – e-20 4 2x - b ifb <x < 2b otherwise ar if x>0 (a > 0) aherwise V2\a + iw) if b <x<c l0 aherwise la-nele - da-iub V2T(a – iw) retar if -b<x<b 7 2 sin b(w – a) lo otherwise if b<x<c bla-w - eila-w) 8 otherwise a - w (a > 0) sin ax 10 if |w| < a; Oif |w| > a (a> 0) 2. 3. 6.
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