# 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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