Answer by Soby for Show that the wave equation takes the form...
First for $r =x + at$ and $s=x-at$, we have $x=\frac{1}{2}(r+s)$ and $t=\frac{1}{2a}(r-s)$. Using chain rule for partial derivatives. For $u:=u(r,s)$, we have \begin{align*}u_s &= u_x \frac{dx}{ds}...
View ArticleShow that the wave equation takes the form $\frac{\partial^2 u}{\partial r...
Show that the wave equation $\frac{\partial^2 u}{\partial t^2} - a^2 \frac{\partial^2 u}{\partial x^2} = 0$ takes the form $\frac{\partial^2 u}{\partial r \partial s} = 0$ under the change of variable...
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