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The following questions concern the classification of second order PDEs. For each question, determine if the given PDE for u = = u(x, y) is parabolic, hyperbolic, or elliptic. If the PDE is of mixed type (that is, could be of more than one type) then you must say when it is parabolic, hyperbolic, or elliptic. a. 2uxx+2Uyy - 4Uxy + Ux + y = 0, b. sin (x)uxx = y²uyy 0 < x, y < 2π 0 ≤ x, y ≤ 1

The following questions concern the classification of second order PDEs. For each question, determine if the given PDE for u = = u(x, y) is parabolic, hyperbolic, or elliptic. If the PDE is of mixed type (that is, could be of more than one type) then you must say when it is parabolic, hyperbolic, or elliptic. a. 2uxx+2Uyy - 4Uxy + Ux + y = 0, b. sin (x)uxx = y²uyy 0 < x, y < 2π 0 ≤ x, y ≤ 1

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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The following questions concern the classification of second order PDEs. For each question, determine if the given PDE for u = u(x, y) is parabolic, hyperbolic, or elliptic. If the PDE is of mixed type (that is, could be of more than one type) then you must say when it is parabolic, hyperbolic, or elliptic. a. 2uxx+2Uyy - 4Uxy + Ux+y=0, 0≤x,y≤1 b. sin (x)uxx = y²Uyy 0< x, y < 2π
Transcribed Image Text:The following questions concern the classification of second order PDEs. For each question, determine if the given PDE for u = u(x, y) is parabolic, hyperbolic, or elliptic. If the PDE is of mixed type (that is, could be of more than one type) then you must say when it is parabolic, hyperbolic, or elliptic. a. 2uxx+2Uyy - 4Uxy + Ux+y=0, 0≤x,y≤1 b. sin (x)uxx = y²Uyy 0< x, y < 2π
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