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Consider the following initial-boundary value problem 4Ut Uzz, 00 %3D U (0, t) U(2, t) = 0 %3D U (1,0) - sin(TI)+ 4 sin(271) 2 sin By the help of the following relation which is found by the separation of variables method X"(x) X(x) 4T'(t) T(t) = -X the solution of the given problem can be found as U(r, t) = Ane-t/4 sin(vAr) %3D n=1 Find the value of U(1, 1)?

Consider the following initial-boundary value problem 4Ut Uzz, 00 %3D U (0, t) U(2, t) = 0 %3D U (1,0) - sin(TI)+ 4 sin(271) 2 sin By the help of the following relation which is found by the separation of variables method X"(x) X(x) 4T'(t) T(t) = -X the solution of the given problem can be found as U(r, t) = Ane-t/4 sin(vAr) %3D n=1 Find the value of U(1, 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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Consider the following initial-boundary value problem 6. 4Ut = Urz, 0<I<2, t >0 0<I<2, t> 0 U (0, t) = U(2, t) = 0 U (r,0) 2 sin () - sin(TI)+ 4 sin(271) 2 10 11 By the help of the following relation which is found by the separation of variables method 12 13 X"(r) 4T' (t) 14 X (x) T(t) 15 16 the solution of the given problem can be found as U (r, t) = Ane-At/4 sin(vAr) n=1 Find the value of U(1, 1)? -2e-n/4 2/4 5,
Transcribed Image Text:Consider the following initial-boundary value problem 6. 4Ut = Urz, 0<I<2, t >0 0<I<2, t> 0 U (0, t) = U(2, t) = 0 U (r,0) 2 sin () - sin(TI)+ 4 sin(271) 2 10 11 By the help of the following relation which is found by the separation of variables method 12 13 X"(r) 4T' (t) 14 X (x) T(t) 15 16 the solution of the given problem can be found as U (r, t) = Ane-At/4 sin(vAr) n=1 Find the value of U(1, 1)? -2e-n/4 2/4 5,
U(1, t) = Ane-t/4 sin(VAr) n=1 Find the value of U(1,1)? O A) -2e-72/4 O B) T/16 2e-2/16 T/4 E)
Transcribed Image Text:U(1, t) = Ane-t/4 sin(VAr) n=1 Find the value of U(1,1)? O A) -2e-72/4 O B) T/16 2e-2/16 T/4 E)
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