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A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with...

A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with radius 2 m and temperature 28°C. The temperature T(r) (in °C) at a distance r (in meters) from the common center of the spheres satisfies the differential equation

d2T
dr2

+

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. (Use T for T(r).)

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