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5 Use the Implicit Function Theorem to prove that there exist C¹ functions u(x, y) and v=v(x, y) defined in some open set V in R² containing the point (1, 1) such that u(1,1)= 1, v(1, 1) = 1, and U= u³+xv² - y = 1, v³+yu² - x = 1 V(x, y) = V.

5 Use the Implicit Function Theorem to prove that there exist C¹ functions u(x, y) and v=v(x, y) defined in some open set V in R² containing the point (1, 1) such that u(1,1)= 1, v(1, 1) = 1, and U= u³+xv² - y = 1, v³+yu² - x = 1 V(x, y) = V.

Advanced Engineering Mathematics
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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#5 Use the Implicit Function Theorem to prove that there exist C¹ functions u= u(x, y) and v = v(x, y) defined in some open set V in R2 containing the point (1, 1) such that u(1,1)= 1, v(1, 1) = 1, and u³+xv² - y = 1, v³+yu²x=1(x, y) = V.
Transcribed Image Text:#5 Use the Implicit Function Theorem to prove that there exist C¹ functions u= u(x, y) and v = v(x, y) defined in some open set V in R2 containing the point (1, 1) such that u(1,1)= 1, v(1, 1) = 1, and u³+xv² - y = 1, v³+yu²x=1(x, y) = V.
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