Solution
= Solution
Each sine product is a Dirichlet eigenfunction. The squared wave-number sums are $24\pi^2$ and $30\pi^2$, respectively, so
$$
\boxed{u=-\frac{\sin(2\pi x)\sin(2\pi y)\sin(4\pi z)}{24\pi^2}
+\frac{\sin(2\pi x)\sin(\pi y)\sin(5\pi z)}{30\pi^2}.}
$$