a sphere with radius of 1meter has a temp = 15degrees. It lies inside a concentric sphere with radius of 2meters and temp = 25degrees. The temp T(r) at a distance r from the common center of the spheres satisfies the differential equation

(d^2T)/dr^2 +(2/r)(dT/dr) = 0

if we let S=dT/dr then S satisfies a first order differential equation. Solve it to find an expression for the temperature T(r) between the spheres.