The diffusion equation

∂c/∂t = D ∂²c/∂x²

where D is a positive constant, describes the diffusion of heat through a solid, or the concentration of a pollutant at time t at a distance x from the source of the pollution, or the invasion of alien species into a new habitat. Verify that the function

c(x,t) = 1/√(4πDt) e⁻ˣ²/⁽⁴ᴰᵗ⁾

is a solution of the diffusion equation.