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1. (a) Consider the equation e'un+2ayury +2e"u- sin(y) u =0, where a is a real constant. Determine the value(s) of a when this equation is elliptic everywhere in the xy-plane, in which case find the canonical variables and reduce the equation to its canonical form.

1. (a) Consider the equation e'un+2ayury +2e"u- sin(y) u =0, where a is a real constant. Determine the value(s) of a when this equation is elliptic everywhere in the xy-plane, in which case find the canonical variables and reduce the equation to its canonical form.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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1. (a) Consider the equation e'ux+2ayuy +2eu,- sin(y) u =0, where a is a real constant. Determine the value(s) of a when this equation is elliptic everywhere in the xy-plane, in which case find the canonical variables and reduce the equation to its canonical form. (b) Find the solution of Laplace's equation outside a unit circle a?u 1 du 0, (r>1,0<0 < 2x), zee e subject to the boundary condition u(1,0) = 2 sin 30, having in mind the requirements that the solution must satisfy in an unbounded domain.
Transcribed Image Text:1. (a) Consider the equation e'ux+2ayuy +2eu,- sin(y) u =0, where a is a real constant. Determine the value(s) of a when this equation is elliptic everywhere in the xy-plane, in which case find the canonical variables and reduce the equation to its canonical form. (b) Find the solution of Laplace's equation outside a unit circle a?u 1 du 0, (r>1,0<0 < 2x), zee e subject to the boundary condition u(1,0) = 2 sin 30, having in mind the requirements that the solution must satisfy in an unbounded domain.
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