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Differential EquationsEasyBoundary Values & Fourier Series

Boundary Values & Fourier Series · Easy problem

A string satisfies utt=9uxxu_{tt} = 9u_{xx} for 0<x<π0 < x < \pi with fixed ends u(0,t)=u(π,t)=0u(0,t) = u(\pi,t) = 0, initial shape u(x,0)=sin⁡2xu(x, 0) = \sin 2x and initial velocity ut(x,0)=0u_t(x, 0) = 0. Find u ⁣(π4,π18)u\!\left(\dfrac{\pi}{4}, \dfrac{\pi}{18}\right).