Determine whether the function is a solution of the wave equation.
-w(x, t) = ln 9cxt

Question

Quizplus · Accepted Answer

The wave equation in two dimensions is given by $\frac{\partial^2 w}{\partial t^2} = c^2 \frac{\partial^2 w}{\partial x^2}$, where $c$ is a constant. The function $w(x, t) = \ln(9cxt)$ does not satisfy this equation because the second derivatives with respect to $x$ and $t$ will not yield proportional results as required by the wave equation. Specifically, the second derivative with respect to $x$ and $t$ of $\ln(9cxt)$ involves terms that do not match the form required by the wave equation, indicating that $w(x, t) = \ln(9cxt)$ is not a solution to the wave equation.

Determine Whether the Function Is a Solution of the Wave