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**Unformatted text preview: **t u du dg x f g(u t x f-= = = = = (In this form it may be seen that any function of this form satisfies the wave equation; see Problem 15.59.) In this case, , ( ) , ( 1 2 2 3-29 + = u A A t x y and so 3 2 2 2 2 3 2 2 2 2 2 3 ) ( ) 3 ( 2 , ) ( 2 u A u A A x y u A u A x y +--= +-= , ) ( ) 3 ( 2 , ) ( 2 2 2 2 2 2 3 2 2 2 2 2 2 3 u A u A A v t y u A u A v t y +--= + = and so the given form for ) , ( t x y is a solution to the wave equation with speed . v...

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