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    Partial differential equations

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    A) Classify and find general expressions for the characteristic coordinates for the equation {see attachment}
    b) Use the canonical coordinates {see attachment} and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that {see attachments} where F and G are arbitrary functions of their arguments.

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    https://brainmass.com/math/partial-differential-equations/partial-differential-equations-38632

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    See attachment

    a) Classify and find general expressions for the characteristic coordinates for the equation

    ( 1)

    b) Use the canonical coordinates and and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that

    where F and G are arbitrary functions of their arguments.

    Solution:
    a) The quadratic terms of the equation (1) are:

    The corresponding characteristic equation is:
    ( 2)
    ( 3)
    Since , the PDE is of hyperbolic type and ...

    Solution Summary

    This shows how to classify and find general expressions for characteristic coordinates and use given canonical coordinates to transfer a partial differential equation to new coordinates.

    $2.49

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