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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(∞) bounded. [Hint: F{8(x)} %3D V2n

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(∞) bounded. [Hint: F{8(x)} %3D V2n

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) (-00 < x < ∞) y(0) = 0, y(∞) bounded. [Hint: F{8(x)} = V2n
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) (-00 < x < ∞) y(0) = 0, y(∞) bounded. [Hint: F{8(x)} = V2n
f(x) f(w) = F(f) %3D SI if-b<x<b 1 2 sin bw lo otherwise S! ifb<x<c lo otherwise -iew -alad (a > 0) 2 a if 0 <x<b -1 + 2ebe – e-20w 2x – b ifb<x< 2b otherwise if x >0 { 1 (a > 0) otherwise V27\a + iw) se ifb<x<c lo aherwise pla-nele – da-iub V27(a – iw) 7| [e if -b<x<b 7 lo otherwise 2 sin b(w – a) w - 8 if b<x<c otherwise gbla-w - eisla-w) 27 a - w 9 (a > 0) Vza sin ax 10 (a > 0) if lwl <a; Oif |삐 >a 2. 3.
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 -iew -alad (a > 0) 2 a if 0 <x<b -1 + 2ebe – e-20w 2x – b ifb<x< 2b otherwise if x >0 { 1 (a > 0) otherwise V27\a + iw) se ifb<x<c lo aherwise pla-nele – da-iub V27(a – iw) 7| [e if -b<x<b 7 lo otherwise 2 sin b(w – a) w - 8 if b<x<c otherwise gbla-w - eisla-w) 27 a - w 9 (a > 0) Vza sin ax 10 (a > 0) if lwl <a; Oif |삐 >a 2. 3.
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