We can divide the equation by a and differentiate a second time to obtain the radiation diffusion equation, cf. eqn (6.95), on replacing the derivative of H in terms of J from eqn (6.114)

where a = 1/3a and b = ยก3/a. For the case of isotropic scattering, g = 0, and for no incoming solar flux a =1/3 and b = 0, and so we obtain the radiation diffusion equation given by eqn (6.97).

If we now substitute for the source function Sx from eqn (6.116) we get a second-order differential equation

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