2. Let us define a. Verify that f(x, y) = c. Now consider the function git Similarly, consider the function g2 af y(x² - y² + 4x²y²) (x² + y²)² dr b. Argue by symmetry that we must have af ду = xy(x² - y²) x² + y² = r(x² - y² - 4x²y²) (x² + y²)² f(0, t). Differentiate this with respect to t to find fry (0,0). s fy(s, 0) and use it to find fyr(0,0).

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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2. Let us define
a. Verify that
f(x, y) =
of
дх
b. Argue by symmetry that we must have
=
xy(x² - y²)
x² + y²
y(x4y² + 4x²y²)
(x² + y²)²
-
dƒ _ x(x² − y¹ − 4x²y²)
(x² + y²)²
ду
c. Now consider the function g₁ : tf(0, t). Differentiate this with respect to t to find fry (0,0).
Similarly, consider the function 92 8 fy(s, 0) and use it to find fyz (0,0).
Transcribed Image Text:2. Let us define a. Verify that f(x, y) = of дх b. Argue by symmetry that we must have = xy(x² - y²) x² + y² y(x4y² + 4x²y²) (x² + y²)² - dƒ _ x(x² − y¹ − 4x²y²) (x² + y²)² ду c. Now consider the function g₁ : tf(0, t). Differentiate this with respect to t to find fry (0,0). Similarly, consider the function 92 8 fy(s, 0) and use it to find fyz (0,0).
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