solve-the-initial-boundary-value-problem-of-wave-equation-2-u-x-t-t-2-9-2-u-x-t-x-2-0-lt-x-lt-2-t-gt-0-u-0-t-1-u-2-t-3-t-gt-0-u-x-0-2-0-lt-x-lt-2-u-t-x-0-sin2x-0-lt-x-lt-2-

Question Number 113271 by mathdave last updated on 12/Sep/20

$${solve}\:{the}\:{initial}\:{boundary}\:{value} \\ $$$${problem}\:{of}\:{wave}\:{equation} \\ $$$$\frac{\partial^{\mathrm{2}} {u}\left({x},{t}\right)}{\partial{t}^{\mathrm{2}} }=\mathrm{9}\frac{\partial^{\mathrm{2}} {u}\left({x},{t}\right)}{\partial{x}^{\mathrm{2}} },\mathrm{0}<{x}<\mathrm{2},{t}>\mathrm{0} \\ $$$${u}\left(\mathrm{0},{t}\right)=\mathrm{1},{u}\left(\mathrm{2},{t}\right)=\mathrm{3},{t}>\mathrm{0} \\ $$$${u}\left({x},\mathrm{0}\right)=\mathrm{2},\mathrm{0}<{x}<\mathrm{2} \\ $$$$\frac{\partial{u}}{\partial{t}}\left({x},\mathrm{0}\right)=\mathrm{sin2}{x},\mathrm{0}<{x}<\mathrm{2} \\ $$

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