?A sphere with radius 1 m has temperature \(15^{\circ} \mathrm{C}\). It lies inside a
Chapter 8, Problem 44(choose chapter or problem)
A sphere with radius 1 m has temperature \(15^{\circ} \mathrm{C}\). It lies inside a concentric sphere with radius 2 m and temperature \(25^{\circ} \mathrm{C}\). The temperature T(r) at a distance r from the common center of the spheres satisfies the differential equation
\(\frac{d^{2} T}{d r^{2}}+\frac{2}{r} \frac{d T}{d r}=0\)
If we let \(S=d T / d r\), then S satisfies a first-order differential equation. Solve it to find an expression for the temperature T(r) between the spheres.
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