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5) Consider the second-order linear partial differential equation. a²u + əx² ' əy² ди ди ду? + 2=+2 = 0 ax ду a) Classify the equation as elliptic, hyperbolic, or parabolic. Show your calculation.

5) Consider the second-order linear partial differential equation. a²u + əx² ' əy² ди ди ду? + 2=+2 = 0 ax ду a) Classify the equation as elliptic, hyperbolic, or parabolic. Show your calculation.

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) Consider the second-order linear partial differential equation. a²u + əx² ди ди ду? + 2=+2 = 0 ax ду a) Classify the equation as elliptic, hyperbolic, or parabolic. Show your calculation. b) Use the separation of variables technique to find the product solution u(x, y) = A(x)B(y). Use the separation constant –1 and suppose that 1< -1. (Do not use the substitution 1 = a²)
Transcribed Image Text:5) Consider the second-order linear partial differential equation. a²u + əx² ди ди ду? + 2=+2 = 0 ax ду a) Classify the equation as elliptic, hyperbolic, or parabolic. Show your calculation. b) Use the separation of variables technique to find the product solution u(x, y) = A(x)B(y). Use the separation constant –1 and suppose that 1< -1. (Do not use the substitution 1 = a²)
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