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    Characteristic curves

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    Find a partial differential equation whose characteristic curves are the lines x-y=a, x+2y=b where a,b are arbitrary real constants.

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    https://brainmass.com/math/partial-differential-equations/characteristic-curves-446928

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    Problem:

    Find a partial differential equation whose characteristic curves are the lines x-y=a, x+2y=b where a,b are arbitrary real constants.

    Solution:

    Since the partial differential equation (PDE) admits real characteristics, then it will be of hyperbolic type, that is:
    ( 1)
    According to the theory, the corresponding equation of the characteristic curves is expressed by:
    ...

    Solution Summary

    The expert finds a partial differential equation whose characteristic curve is a line.

    $2.19