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(a) Consider the equation e'ux+2ayuy +2e*uy-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.

(a) Consider the equation e'ux+2ayuy +2e*uy-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.

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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1(A)

(a) Consider the equation e'un+2ayuy +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 ry-plane, in which case find the canonical variables and reduce the equation to its canonical form.
Transcribed Image Text:(a) Consider the equation e'un+2ayuy +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 ry-plane, in which case find the canonical variables and reduce the equation to its canonical form.
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