Consider the following initial-boundary value problem 4Ut Urz, 00 %3D U (0, t) U(2, t) = 0 U(1,0) 2 sin ()- sin(7I) + 4 sin(2r1) %3D By the help of the following relation which is found by the separation of variables method X"(x) _ 4T'(t) %3D %3D X(x) T(t) the solution of the given problem can be found as U(r,t) = A,ne-t/4 sin(vAr) %3D n=1 Find the value of U(1,1)?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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13. Soru
7 Puan
Consider the following initial-boundary value problem
4U
Ura, 0<I< 2, t>0
%3D
U (0, t)
U (2, t) =0
%3D
U(1,0)
2 sin
) - sin(rx) +4 sin(2T1)
%3D
By the help of the following relation which is found by the separation of variables method
X"(x)
X(r)
4T' (t)
T(t)
%3D
the solution of the given problem can be found as
U(r,t) =Ane-M/4 sin(vAr)
n-1
Find the value of U(1, 1)?
O A)
-e-7/4
2e-a/16
Transcribed Image Text:13. Soru 7 Puan Consider the following initial-boundary value problem 4U Ura, 0<I< 2, t>0 %3D U (0, t) U (2, t) =0 %3D U(1,0) 2 sin ) - sin(rx) +4 sin(2T1) %3D By the help of the following relation which is found by the separation of variables method X"(x) X(r) 4T' (t) T(t) %3D the solution of the given problem can be found as U(r,t) =Ane-M/4 sin(vAr) n-1 Find the value of U(1, 1)? O A) -e-7/4 2e-a/16
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