We had a quiz in class today, and one of the questions was:
"Is $Ae^(kx-\omega t)$ a solution to the wave equation?" My thought process said: A) It's missing $i$ so it's not a simple sin/cos function in Euler's form. And, if I rewrite the equation to $Ae^{kx}e^{-\omega t}$, then if I fix a value of $t$, like $t = 0$, the $Ae^{kx-\omega t} \to \infty$ as $x \to \infty$. Waves don't gain infinite amplitude, right? But it looks like I got the problem wrong, because differentiation satisfies the wave PDE. Could someone explain what I'm missing?