  The wave equation $\left(\partial_{tt} - c^2 \Delta_x\right) u(x,t) = e^{-t}
f(x,t)$ is shown to have a unique solution if $u$ and its partial derivatives
in $x$ are in $L^2(e^{-t})$ on the cone, and the solution can be explicit given
in the Fourier series of orthogonal polynomials on the cone. This provides a
particular solution for the boundary value problems of the non-homogeneous wave
equation on the cone, which can be combined with a solution to the homogeneous
wave equation in the cone to obtain the full solution.
