Answered: Solve the problem in Example 1 if…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Solve the problem in Example 1 if

Write out the first four nonzero terms of the series solution. [Hint: See Example 3, Section 12.6.]

Example 1

Find the steady-state temperature u(r, θ) in the sphere shown in FIGURE 14.3.2.

Expert Solution

Step 1

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Given that $f (θ) = \{\begin{cases} 50 & 0 < θ < π / 2 \\ 0 & π / 2 < θ < π \end{cases}$

It is known that

$\begin{array}{rcl} a_{0} & = & \frac{1}{π} \int_{0}^{π} f (x) d x \\ = & \frac{1}{π} {[50 x]}_{0}^{π / 2} \\ = & \frac{1}{π} [25 π] \\ = & 25 \end{array}$

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