APM346-2015S > Web Bonus Problems

Web Bonus Problem 2

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Victor Ivrii:
Solve
\begin{align}
&(t^2+1)u_{tt}+tu_t-u_{xx}=0,\label{eq-1}\\[3pt]
&u|_{t=0}=0, \qquad u_t|_{t=0}=1.\label{eq-2}
\end{align}
Hint: Make a change of variables $x=\frac{1}{2}(\xi+\eta)$, $t=\sinh (\frac{1}{2}(\xi-\eta))$ and calculate $u_\xi$, $u_\eta$, $u_{\xi\eta}$.

Yiyun Liu:
pro，I think there is a type error of the hint you provide, should x=(xi+eta)/2 instead of xi=(xi+eta)/2 ?
thx

Thanks, corrected. V.I.

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