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a. Classify the PDE given by 3uxx - U xy + Uyy = 0 b. Determine the transformation variables that will permit the transformation of the equation of part (a) into canonical form. It is not necessary to carry out the transformation. c. Express the PDE of part (a) as an equivalent system of first-order equations.

a. Classify the PDE given by 3uxx - U xy + Uyy = 0 b. Determine the transformation variables that will permit the transformation of the equation of part (a) into canonical form. It is not necessary to carry out the transformation. c. Express the PDE of part (a) as an equivalent system of first-order equations.

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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a. Classify the PDE given by 3uxx - U xy + Uyy = 0 b. Determine the transformation variables that will permit the transformation of the equation of part (a) into canonical form. It is not necessary to carry out the transformation. c. Express the PDE of part (a) as an equivalent system of first-order equations.
Transcribed Image Text:a. Classify the PDE given by 3uxx - U xy + Uyy = 0 b. Determine the transformation variables that will permit the transformation of the equation of part (a) into canonical form. It is not necessary to carry out the transformation. c. Express the PDE of part (a) as an equivalent system of first-order equations.
Expert Solution
Step 1: Definition

Let Auxx+Buxy+Cuyy=F(x,y,u,ux,uy) be a second order partial differential equation  .

  • If B2−4AC<0 , then pde is elliptic .
  • If B2−4AC=0 , then pde is parabolic .
  • If B2−4AC>0 , then pde is hyperbolic .
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