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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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23

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Integral equations

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23.1  Solve the integral equation

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for the function y = y(x) for x > 0. Note that for x < 0, y(x) can be chosen as is most convenient.

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Since cos uv is an even function of v, we will make y(−v) = y(v) so that the complete integrand is also an even function of v. The integral I on the LHS can then be written as

the last step following ...

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