(a) Use the method of characteristics to solve the following boundary-value problem: - yur(x, y) = xuy(x, y) = 0, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Use the method of characteristics to solve the following boundary-value
problem:
-
yur(x, y) = xuy(x, y) = 0, 0<x, 0<y,
u(0, y) = 4 sin(y²) +1, 0≤y
for the function u(x, y).
(b) Verify that the solution you found in part (a) solves the partial differential equa-
tion and the boundary condition in part (a).
(c) Sketch and label a representative sample of the characteristic curves in part (a)
and explain how this shows that the method of characteristics gives us a solution
of the boundary-value problem in part (a).
Transcribed Image Text:(a) Use the method of characteristics to solve the following boundary-value problem: - yur(x, y) = xuy(x, y) = 0, 0<x, 0<y, u(0, y) = 4 sin(y²) +1, 0≤y for the function u(x, y). (b) Verify that the solution you found in part (a) solves the partial differential equa- tion and the boundary condition in part (a). (c) Sketch and label a representative sample of the characteristic curves in part (a) and explain how this shows that the method of characteristics gives us a solution of the boundary-value problem in part (a).
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