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    Fourier Transforms and Convolution Theorem

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    Consider the ODE
    .....
    with the boundary conditions
    y(x) bounded as....
    Assume that b is real and positive and that g(x) behaves in such a way so that a bounded solution is
    possible.
    (a) Compute the Fourier transform of the solution
    (b) Use the convolution theorem to solve the ODE and express the solution as an integral involving g(x).

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    © BrainMass Inc. brainmass.com October 9, 2019, 10:53 pm ad1c9bdddf
    https://brainmass.com/math/fourier-analysis/fourier-transforms-convolution-theorem-235579

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    (1) Since given equation is

    Now taking Fourier Transform

    Both ...

    Solution Summary

    The expert examines Foruier transforms and convolution theorems.

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