Chapter 9.3, Problem 42E

A sphere with radius 1 m has temperature 15°C. It lies inside a concentric sphere with radius 2 m and temperature 25°C. The temperature T(r) at a distance r from the common center of the spheres satisfies the differential equation

$\frac{d^{2}T}{d{r}^2}+\frac{2}{r}\frac{dT}{dr}=0$

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.