# Toronto Math Forum

## APM346-2015S => APM346--Home Assignments => Web Bonus Problems => Topic started by: Victor Ivrii on January 14, 2015, 09:20:14 AM

Title: Web Bonus Problem 2
Post by: Victor Ivrii on January 14, 2015, 09:20:14 AM
Solve
\begin{align}
&(t^2+1)u_{tt}+tu_t-u_{xx}=0,\label{eq-1}\\[3pt]
Hint: Make a change of variables $x=\frac{1}{2}(\xi+\eta)$, $t=\sinh (\frac{1}{2}(\xi-\eta))$ and calculate $u_\xi$, $u_\eta$, $u_{\xi\eta}$.