Chapter 13.10, Problem 23MP

Find the steady-state temperature in the region between two spheres $r=1$ and $r=2$ if the surface of the outer sphere has its upper half held at ${100}^{°}$ and its lower half at $-{100}^{°}$ and these temperatures are reversed for the inner sphere. Hint: See Problem 7.14. Here you will need to find two Legendre series (when $r=1$ and when $r=2)$ and solve for $a_1$ and $b_1$.