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
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Chapter2: Second-order Linear Odes
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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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