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1. Classify each of the partial differential equations below as either hyperbolic, parabolic, or elliptic, determine the characteristics, and transform the equations to canonical form: (g) x²uxx+4yux+u+2u₁ = 0, (i) Uxx+2xU¸+ a²u+u = 5, (h) 3yux-xu = 0, (j) yuxx-2u+e* U + x² u₂ − u = 0. yy

1. Classify each of the partial differential equations below as either hyperbolic, parabolic, or elliptic, determine the characteristics, and transform the equations to canonical form: (g) x²uxx+4yux+u+2u₁ = 0, (i) Uxx+2xU¸+ a²u+u = 5, (h) 3yux-xu = 0, (j) yuxx-2u+e* U + x² u₂ − u = 0. yy

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. Classify each of the partial differential equations below as either hyperbolic, parabolic, or elliptic, determine the characteristics, and transform the equations to canonical form: (g) x²uxx+4yu+u+2u, = 0, (i) uxx + 2xu + a²u+u = 5, Ux xy (h) 3yux-xu = 0, хи yy - (j) yux-2u + e*u, + x² u₂ − u = 0. xy
Transcribed Image Text:1. Classify each of the partial differential equations below as either hyperbolic, parabolic, or elliptic, determine the characteristics, and transform the equations to canonical form: (g) x²uxx+4yu+u+2u, = 0, (i) uxx + 2xu + a²u+u = 5, Ux xy (h) 3yux-xu = 0, хи yy - (j) yux-2u + e*u, + x² u₂ − u = 0. xy
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