Suppose that the function u(x, y) is solution of the problem = 0, 1²+1² < 25, ox² ay² u(x, y) = 5(x - y)²-12xy, x² + y² = 25 (a) Find the maximum value of u(x, y) on the closed disk {(x, y), x² +₁₁² ≤ 25}. (b) Find the minimum value of u(x, y) on the closed disk {(x, y), x² + y² ≤ 25}. (c) What is the value of u(0, 0)?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem #2: Suppose that the function u(x, y) is solution of the problem
= 0, 1²+1² < 25,
5(x - y)²2²-12xy, x²² +1²²= 25
+
- u(x, y) =
<
(a) Find the maximum value of u(x, y) on the closed disk {(x, y), x² +₁₁² ≤ 25}.
(b) Find the minimum value of u(x, y) on the closed disk {(x, y), x² + y² ≤ 25}.
(c) What is the value of u(0, 0)?
Transcribed Image Text:Problem #2: Suppose that the function u(x, y) is solution of the problem = 0, 1²+1² < 25, 5(x - y)²2²-12xy, x²² +1²²= 25 + - u(x, y) = < (a) Find the maximum value of u(x, y) on the closed disk {(x, y), x² +₁₁² ≤ 25}. (b) Find the minimum value of u(x, y) on the closed disk {(x, y), x² + y² ≤ 25}. (c) What is the value of u(0, 0)?
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