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    Vibrating String and d'Alembert's Solution in Wave Equation

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    2. Show that, like the wave equation, the given PDE is hyperbolic and find its general solution by introducing the suggested change of variables.
    (b) uxx - 4uxy - 5uyy = 0 ........
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    (b)

    Solution. Introduce new variables

    Use chain rule, we have

    and

    So,

    ...

    Solution Summary

    A PDE is shown to be hyperbolic and its general solution is found by introducing a suggested change of variables. The solution is detailed and well presented.

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