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Differential EquationsMediumBoundary Values & Fourier Series

Boundary Values & Fourier Series · Medium problem

A rod 0≤x≤π0 \le x \le \pi with both ends insulated, ux(0,t)=ux(π,t)=0u_x(0, t) = u_x(\pi, t) = 0, obeys ut=uxxu_t = u_{xx} and starts at u(x,0)=2+cos⁡2xu(x, 0) = 2 + \cos 2x. Find the temperature at the left end at time t=ln⁡34t = \dfrac{\ln 3}{4}.