The Green function G(x, y, z, t > 0) = (t r/c)/4r is a solution of

The Green function G(x, y, z, t > 0) = δ(t − r/c)/4πr is a solution of the inhomogeneous wave equation in three space dimensions with the source term −δ(x)δ(y)δ(z)δ(t).
(a) Show that G₂(x, y, t) = ∫^∞ _−∞ dz G(x, y, z, t) is a solution of the inhomogeneous wave equation in two space dimensions with the source term −δ(x)δ(y)δ(t).
(b) Evaluate the integral in part (a) to find G₂(ρ, t) explicitly, where ρ² = x² + y².