A sphere with radius 1 m has temperature 12°C. It lies inside a concentric sphere with radius 2 m and temperature 21°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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.