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Consider the equation where q(y) -1. 0, 1. y < -1 |y| ≤1. y > 1 i) Find the domains where the equation is hyperbolic, parabolic, and elliptic. ii) For each of the above three domains, find the corresponding canonical transformation and the canonical form. = Uxx + 2Uxy + (1-q(y))uyy = 0

Consider the equation where q(y) -1. 0, 1. y < -1 |y| ≤1. y > 1 i) Find the domains where the equation is hyperbolic, parabolic, and elliptic. ii) For each of the above three domains, find the corresponding canonical transformation and the canonical form. = Uxx + 2Uxy + (1-q(y))uyy = 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 19RE
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Consider the equation where q(y) - 0, 1. y < −1 |y| ≤ 1. y > 1 Uxx + 2Uxy + (1 − q(y))Uyy ² = 0 i) Find the domains where the equation is hyperbolic, parabolic, and elliptic. ii) For each of the above three domains, find the corresponding canonical transformation and the canonical form.
Transcribed Image Text:Consider the equation where q(y) - 0, 1. y < −1 |y| ≤ 1. y > 1 Uxx + 2Uxy + (1 − q(y))Uyy ² = 0 i) Find the domains where the equation is hyperbolic, parabolic, and elliptic. ii) For each of the above three domains, find the corresponding canonical transformation and the canonical form.
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