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ôu a?u Let u be the unique solution of where (x, t) e (0, 1) x (0, 0), u(x, 0) = %3D sin Tx, x e (0, 1) u(0, t) = u(1, t) = 0t e (0, 0) Then which of the following are true? (a) 3 (x, t) e (0, 1) × (0, o) s.t. u(x, t) = 0 ди (x,1) =0 ốt (b) 3 (x, t) e (0, 1) x (0, c0) s.t. (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) x (0, 0)

ôu a?u Let u be the unique solution of where (x, t) e (0, 1) x (0, 0), u(x, 0) = %3D sin Tx, x e (0, 1) u(0, t) = u(1, t) = 0t e (0, 0) Then which of the following are true? (a) 3 (x, t) e (0, 1) × (0, o) s.t. u(x, t) = 0 ди (x,1) =0 ốt (b) 3 (x, t) e (0, 1) x (0, c0) s.t. (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) x (0, 0)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.3: Euler's Method
Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.
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If u(x, t) is a solution of u, = uxx * u(x, 0) = 1+ x+ sin (ax) cos (Tx) u(0, t) = 1, u(1, t) = 2. Then 0 <x<1 t>0 (a) u 2 4 3 3 (b) u 4 4 1 -37? +-e 4 2 1 --472 (c) u (e) (d) и 4 +-e 4
Transcribed Image Text:If u(x, t) is a solution of u, = uxx * u(x, 0) = 1+ x+ sin (ax) cos (Tx) u(0, t) = 1, u(1, t) = 2. Then 0 <x<1 t>0 (a) u 2 4 3 3 (b) u 4 4 1 -37? +-e 4 2 1 --472 (c) u (e) (d) и 4 +-e 4
ôu a?u Let u be the unique solution of where (x, t) e (0, 1) x (0, 0), u(x, 0) = sin Tx, x e (0, 1) u(0, t) = u(1, t) 0t e (0, 0) Then which of the following are true? !! (a) 3 (x, t) e (0, 1) x (0, 0) s.t. u(x, t) = 0 (b) 3 (x, t) e (0, 1) x (0, o) s.t. ди (x,()%3D0 (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) × (0, 0) (d) 3 (x, t) e (0, 1) x(0, 0) s.t. u(x, t) > 1
Transcribed Image Text:ôu a?u Let u be the unique solution of where (x, t) e (0, 1) x (0, 0), u(x, 0) = sin Tx, x e (0, 1) u(0, t) = u(1, t) 0t e (0, 0) Then which of the following are true? !! (a) 3 (x, t) e (0, 1) x (0, 0) s.t. u(x, t) = 0 (b) 3 (x, t) e (0, 1) x (0, o) s.t. ди (x,()%3D0 (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) × (0, 0) (d) 3 (x, t) e (0, 1) x(0, 0) s.t. u(x, t) > 1
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