Problem 1. Let a € R and u solve the 2nd order linear partial differential equation Uzz – 2auzy – 3a°uyy + uz + au, = 0. (A) Classify the type of equation for (1.1) according to the value of a. (1.1) (B) Transform (1.1) into the canonical form and solve the equation. | (Hint: the type of equation may depend on the value of a, and you may need to divide the discussion into several cases.)
Problem 1. Let a € R and u solve the 2nd order linear partial differential equation Uzz – 2auzy – 3a°uyy + uz + au, = 0. (A) Classify the type of equation for (1.1) according to the value of a. (1.1) (B) Transform (1.1) into the canonical form and solve the equation. | (Hint: the type of equation may depend on the value of a, and you may need to divide the discussion into several cases.)
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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Transcribed Image Text:Problem 1. Let a e R and u solve the 2nd order linear partial differential
equation
Uzz – 2auzy – 3a²uyy + Uz + auy = 0.
(A) Classify the type of equation for (1.1) according to the value of a.
(1.1)
(B) Transform (1.1) into the canonical form and solve the equation. |
(Hint: the type of equation may depend on the value of a, and you may need to
divide the discussion into several cases.)
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