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Consider the partial differential equation J²u ?u მე2 Ət = with boundary conditions u(0, t) = 0 and u(π, t) = 0 for t≥ 0, and the initial condition 4 1 +++) 4 The general solution that satisfies the boundary conditions is u(x, 0): = x -x + u(x, t) = Ane-16n²t sin(4nx). n=1 Select the option that gives the correct method for determining the constants An from the given initial condition. Select one: An 1 4 An * = 1/2 √ ³* = ( − 2 + + x) sin(dnxx) dx. = An = 00 1 7 4 S 0 ㅠ 8 T 8 4 A₁ = 2/¹² = (-2+ + x) cos(inz) de An ㅠ 0 - π 4 1 T x :(- -x+17) cos(4nx) dx π € (-² -x+r) sin(4nx) dx 8 4 A₂ = 2 * = (-2+ +*) sin(4x) da An π 0

Consider the partial differential equation J²u ?u მე2 Ət = with boundary conditions u(0, t) = 0 and u(π, t) = 0 for t≥ 0, and the initial condition 4 1 +++) 4 The general solution that satisfies the boundary conditions is u(x, 0): = x -x + u(x, t) = Ane-16n²t sin(4nx). n=1 Select the option that gives the correct method for determining the constants An from the given initial condition. Select one: An 1 4 An * = 1/2 √ ³* = ( − 2 + + x) sin(dnxx) dx. = An = 00 1 7 4 S 0 ㅠ 8 T 8 4 A₁ = 2/¹² = (-2+ + x) cos(inz) de An ㅠ 0 - π 4 1 T x :(- -x+17) cos(4nx) dx π € (-² -x+r) sin(4nx) dx 8 4 A₂ = 2 * = (-2+ +*) sin(4x) da An π 0

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 partial differential equation J²u ?u მე2 Ət = with boundary conditions u(0, t) = 0 and u(π, t) = 0 for t > 0, and the initial condition 4 1 +++) 4 The general solution that satisfies the boundary conditions is u(x, 0): = x -x + u(x, t) = Ane-16n²t sin(4nx). n=1 Select the option that gives the correct method for determining the constants An from the given initial condition. Select one: An 1 4 An * = 1/2 √ ³* = ( − 2 + + x) sin(dnxx) dx. = An = 00 1 7 4 S 0 ㅠ 8 T 8 4 A₁ = 2/¹² = (-2+ + x) cos(inz) de An ㅠ 0 - π 4 1 T x :(- -x+17) cos(4nx) dx π € (-² -x+r) sin(4nx) dx 8 4 A₂ = 2 * = (-2+ +*) sin(4x) da An π 0
Transcribed Image Text:Consider the partial differential equation J²u ?u მე2 Ət = with boundary conditions u(0, t) = 0 and u(π, t) = 0 for t > 0, and the initial condition 4 1 +++) 4 The general solution that satisfies the boundary conditions is u(x, 0): = x -x + u(x, t) = Ane-16n²t sin(4nx). n=1 Select the option that gives the correct method for determining the constants An from the given initial condition. Select one: An 1 4 An * = 1/2 √ ³* = ( − 2 + + x) sin(dnxx) dx. = An = 00 1 7 4 S 0 ㅠ 8 T 8 4 A₁ = 2/¹² = (-2+ + x) cos(inz) de An ㅠ 0 - π 4 1 T x :(- -x+17) cos(4nx) dx π € (-² -x+r) sin(4nx) dx 8 4 A₂ = 2 * = (-2+ +*) sin(4x) da An π 0
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