A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with radius 2 m and temperature 19°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
A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with radius 2 m and temperature 19°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
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Calc 2:
A sphere with radius 1 m has temperature 11°C. It lies inside a concentric sphere with radius 2 m and temperature 19°C. The temperature T(r) (in °C) at a distance r (in meters) from the common center of the spheres satisfies the
d2T |
dr2 |
2 |
r |
dT |
dr |
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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