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3. Using the method of characteristics, find a solution to the following problems: (i) x²u + xyuy + xu = x – y with u = 1 - on y = x. (ii) x(y – u)u + y(x + u)uy = (x + y)u with u = x² +1 on y = x.

3. Using the method of characteristics, find a solution to the following problems: (i) x²u + xyuy + xu = x – y with u = 1 - on y = x. (ii) x(y – u)u + y(x + u)uy = (x + y)u with u = x² +1 on y = x.

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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3. Using the method of characteristics, find a solution to the following problems: 1 (i) х*и, + уu, + хи — х —у with и — — on y —х. (ii) a(у — и)и, + y(х + u)u, — (х +у)и with u %3D 2? +1 on y %3 х.
Transcribed Image Text:3. Using the method of characteristics, find a solution to the following problems: 1 (i) х*и, + уu, + хи — х —у with и — — on y —х. (ii) a(у — и)и, + y(х + u)u, — (х +у)и with u %3D 2? +1 on y %3 х.
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