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#### superbread88

##### New member

- Dec 19, 2012

- 2

Have been trying for hours but simply no results. Hope that someone can help me out.

\[\frac{\partial u}{\partial t}=4\frac{\partial^2 u}{\partial x^2}\]

for \(t>0\) and \(0\leq x\leq 2\) subject to the boundary conditions

\[u_x (0,t) = 0\mbox{ and }u(2,t) = 0\]

and the initial condition

\[u(x,0) = 2 \cos \left(\frac{7\pi x}{4}\right)\]

By the use of separations of variables, solve the above equation for the temperature \(u(x,t)\)

\[\frac{\partial u}{\partial t}=4\frac{\partial^2 u}{\partial x^2}\]

for \(t>0\) and \(0\leq x\leq 2\) subject to the boundary conditions

\[u_x (0,t) = 0\mbox{ and }u(2,t) = 0\]

and the initial condition

\[u(x,0) = 2 \cos \left(\frac{7\pi x}{4}\right)\]

By the use of separations of variables, solve the above equation for the temperature \(u(x,t)\)

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