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    Verify that (6-85a) and (6-85b) are solutions to (6-84a).

    6-84a:

    The partial derivative has been replaced by the ordinary derivative since is only a function of the radial coordinate.
    The differential equation 6-84a has two independent solutions

    6-85a:

    6-85b:

    Equation 6-85a represents an outwardly (in the radial direction) traveling wave and (6-85b) describes an inwardly traveling wave, assuming time variations.

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    https://brainmass.com/math/derivatives/traveling-wave-verify-equation-171066

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    Please see the attached file.

    Verify that (6-85a) and (6-85b) are solutions to (6-84a).

    6-84a:

    The partial derivative has been replaced by the ordinary derivative since is only a function ...

    Solution Summary

    It verifies that the traveling wave equations are solution to a differential equation. The solution is detailed and was rated '5/5' by the student who posted the question originally.

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