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# A sphere with radius 1 m has temperature $15^oC.$ It lies inside a concentric sphere with radius 2 m and temperature $25^oC.$ The temperature $T(r)$ at a distance $r$ from the common center of the spheres satisfies the differential equation $\frac {d^2T}{dr^2} + \frac {2}{r}\frac {dT}{dr} = 0$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.

## $T(r)=\frac{-20}{r}+35$

#### Topics

Differential Equations

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

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Other Schools

#### Topics

Differential Equations

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp