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Solve $$\frac{\partial u}{\partial t} = 2\frac{\partial^2 u}{\partial x^2}$$ with $0 < x < 3, t > 0$, given that $u(0,t) = u(3,t) = 0$, and $$u(x,0) = 5\sin 4\pi x - 3\sin 8\pi x + 2\sin 10 \pi x.$$ Note that $u(x,t)$ is bounded.

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    Welcome to Math.SE! A few guidelines on getting the best help from the community possible: **What have you done so far? What do you know?** If you can support your questions with answers to these two questions, you will be more likely to receive the best help.2012-11-28
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    Use separation of variables.2012-11-28
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    Do you know the general form of the solution to the heat equation? If so, then it will be very quick to read off the Fourier coefficients and get a full exact solution.2012-11-28
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    This question has been solved perfectly. Hope that the asker has been diving enough and accept the answer at an early date.2013-04-21

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