Heat Diffusion Equation and Standard Heat Equation

Note: Please do not reply to this posting unless you are willing to
explain your solution. I do not understand how to solve, so I need an
explanation along with the solution. (Too often, important steps are
omitted thereby rendering the solution useless to me.) Thank you in
advance!



Let the temperature u inside a solid sphere be a function only of radial
distance r from the center and time t. Show that the equation for heat
diffusion is now

.



This is not an exercise in doing a polar coordinate
transformation. First you should derive an integral form for the
equation

by integrating over an appropriate domain. Then from this obtain
the differential equation.

for a suitable choice of m can be used to reduce this equation to the


standard heat equation.