# Fourier Transforms and Convolution Theorem

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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(1) Since given equation is

Now taking Fourier Transform

Both ...

#### Solution Summary

The expert examines Foruier transforms and convolution theorems.

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