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 2 329 + = 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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 Calculus, Derivative, Partial differential equation, wave equation, dg u dg, dg f dg

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