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PROBLEM 1 Use the method of separation of variables to solve ди ди - = 0 in (0,1)× (0,+0), (1) ди u(0,1) = 0," (1,1) = 0,1 > 0, u(x,0) = x,0 0, (2) ди ди u(x,0,1) =u(x,1,1) = 0,0 0, dy (u(x, y,0) = 1, (x, y) e (0,1).

PROBLEM 1 Use the method of separation of variables to solve ди ди - = 0 in (0,1)× (0,+0), (1) ди u(0,1) = 0," (1,1) = 0,1 > 0, u(x,0) = x,0 0, (2) ди ди u(x,0,1) =u(x,1,1) = 0,0 0, dy (u(x, y,0) = 1, (x, y) e (0,1).

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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PROBLEM 1 Use the method of separation of variables to solve ди ди - = 0 in (0,1)× (0,+0), (1) ди u(0,1) = 0," (1,1) = 0,1 > 0, u(x,0) = x,0 <x <l. PROBLEM 2 Use the method of separation of variables to solve ôu v'u = 0 in (0,1)² × (0,+∞), u(0, y,1) = u(1, y,t) = 0,0 < y < 1,1 > 0, (2) ди ди u(x,0,1) =u(x,1,1) = 0,0 <x <1,1 > 0, dy (u(x, y,0) = 1, (x, y) e (0,1).
Transcribed Image Text:PROBLEM 1 Use the method of separation of variables to solve ди ди - = 0 in (0,1)× (0,+0), (1) ди u(0,1) = 0," (1,1) = 0,1 > 0, u(x,0) = x,0 <x <l. PROBLEM 2 Use the method of separation of variables to solve ôu v'u = 0 in (0,1)² × (0,+∞), u(0, y,1) = u(1, y,t) = 0,0 < y < 1,1 > 0, (2) ди ди u(x,0,1) =u(x,1,1) = 0,0 <x <1,1 > 0, dy (u(x, y,0) = 1, (x, y) e (0,1).
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