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To solve the wave equation de una 4. u,(0, 1)-0, u,(3, 1)-0, u(x,0)=sin()u₂(x, 0)-0 the nontrivial solutions of X-equation and T-equation are: Note: the separation constant is - X(x) = A cos(x) and (t) = C cos (32) O Xx) = A cosh(x) and (t) = C cos(1) x(x) = 8 sin(x) and (t) = D sin (2) x(x) = A cos(x) and (t) = C cos (1)

To solve the wave equation de una 4. u,(0, 1)-0, u,(3, 1)-0, u(x,0)=sin()u₂(x, 0)-0 the nontrivial solutions of X-equation and T-equation are: Note: the separation constant is - X(x) = A cos(x) and (t) = C cos (32) O Xx) = A cosh(x) and (t) = C cos(1) x(x) = 8 sin(x) and (t) = D sin (2) x(x) = A cos(x) and (t) = C cos (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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QUESTION 1 a²u 4 a²u To solve the wave equation x² 32²,(0,1)=0, u,(3, 1)-0. u(x, 0)=sin()u(x,0)=0 the nontrivial solutions of X-equation and T-equation are: Note: the separation constant is-A x(x) = A cos(x) and 7(t) = C cos (32) X(x) = A cosh (x) and (t) = C cos(17) O x(x) = 8 sin(x) and (t) = sin(2) D X(x) = A cos(x) and (t) = C cos ( 1 )
Transcribed Image Text:QUESTION 1 a²u 4 a²u To solve the wave equation x² 32²,(0,1)=0, u,(3, 1)-0. u(x, 0)=sin()u(x,0)=0 the nontrivial solutions of X-equation and T-equation are: Note: the separation constant is-A x(x) = A cos(x) and 7(t) = C cos (32) X(x) = A cosh (x) and (t) = C cos(17) O x(x) = 8 sin(x) and (t) = sin(2) D X(x) = A cos(x) and (t) = C cos ( 1 )
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