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Solve the boundary value problem $$\begin{cases} \displaystyle \frac{\partial u}{\partial t} = 2 \frac{\partial^2 u}{\partial x^2} \\ \ \\u(0,t) = 10 \\ u(3,t) = 40 \\ u(x, 0) = 25 \end{cases}$$

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    This uses separation of variables and Fourier series. I am sure there are many resources you can find online telling you how to solve a problem like this.2012-11-28

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