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If the Fourier transform of f(x) is ƒ(k), show that the Fourier transform of ƒ(x) is f(−k). Hint: the inverse Fourier transform may be useful here Use a Fourier transform technique to solve the Airy equation u" (x) = xu(x) by finding a integral formula for u(x).

If the Fourier transform of f(x) is ƒ(k), show that the Fourier transform of ƒ(x) is f(−k). Hint: the inverse Fourier transform may be useful here Use a Fourier transform technique to solve the Airy equation u" (x) = xu(x) by finding a integral formula for u(x).

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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7. (a) If the Fourier transform of f(x) is f(k), show that the Fourier transform of ƒ(x) is f(−k). Hint: the inverse Fourier transform may be useful here Use a Fourier transform technique to solve the Airy equation (b) u"(x) = xu(x) by finding a integral formula for u(x).
Transcribed Image Text:7. (a) If the Fourier transform of f(x) is f(k), show that the Fourier transform of ƒ(x) is f(−k). Hint: the inverse Fourier transform may be useful here Use a Fourier transform technique to solve the Airy equation (b) u"(x) = xu(x) by finding a integral formula for u(x).
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