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
(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
The expert examines Foruier transforms and convolution theorems.