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I need to solve this:

$ \begin{cases} U_{tt}= \Delta U + |x|^2 \sin t \\ U(x,0) = |x|^4 + |x|^2 \\ U_t(x,0) = |x|^4 - |x|^2 \end{cases} $

in 3 dimensions $x = \{x_1, x_2, x_3\}$

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    Does $|x|=\sqrt{x_1^2+x_2^2+x_3^2}$ ?2012-12-21

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Try solutions of the form $U(x,t) = (6-|x|^2) \sin(t) + \dfrac{F(|x|+t)+ G(|x|-t)}{|x|}$

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    Hmm, didn't notice how old this question was. @night-owl: why did you edit it now? Are you interested in a solution?2012-07-05