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Prove that $u=e^{-4t}\cos\omega x$ is a solution of the one-dimensional wave equation $\frac{\partial u}{\partial t}=c^2\frac {\partial^2 u }{\partial x^2}.$ I found $\frac{\partial u }{\partial t}=-4e^{-4t}\cos\omega x$ and $\frac{\partial^2 u}{\partial x^2}=-\omega^2e^{-4t}\cos\omega x$ but I can't equate the two. Please help to find a solution.

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    @Daryl thanks for telling the mistake and you are right it was happened because of my carelessness2012-08-12

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I guess this means you have to find $\omega$ so that $u=e^{−4t}\cos\omega x$ satisfies $u_t=c^2u_{xx}$? By the way, this is called a heat equation, not a wave equation.

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    w is +2 or -2 what's next2013-03-08