Stefan's Law of Radiation states that the radiation energy of abody is proportional to the fourth power of the absolute temperature T of a body. The rate of change of this energy ina surrounding medium of absolute temperature M is thus

$\frac{dT}{dt}=k({M}^{4}-{T}^{4})$

where k > 0 is a constant. Show that the general solution of Stefan's equation is

$\mathrm{ln}|\frac{M+T}{M-T}|+2{\mathrm{tan}}^{-1}(\frac{T}{M})=4{M}^{3}kt+c$

where c is an arbitrary constant.

$\frac{dT}{dt}=k({M}^{4}-{T}^{4})$

where k > 0 is a constant. Show that the general solution of Stefan's equation is

$\mathrm{ln}|\frac{M+T}{M-T}|+2{\mathrm{tan}}^{-1}(\frac{T}{M})=4{M}^{3}kt+c$

where c is an arbitrary constant.