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Consider the partial differential equation 2² u du dx² Ət with boundary conditions u(0, ₺) = 0 and 1 |u(π, t) un, t) = 0 for t≥ 0, and the initial condition u(x, 0) = X u(r, t) The general solution that satisfies the boundary conditions is Select one: An Ane-16n²t Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An = = = = - = 4 7 8 T > 4 +x. TT ∞ Σ n=1 TT 1 4 1 8 4 ³/16.* π 4 4 ſ 0 1 4 1 8 4 T T π 7T 1 T) 4 IT T • (-x x X sin(4nx). X (-x + 1/7) sin(4nx) dx -x+¹) sin(4x) dx X (-x+ r) cos(4nx) dx -x+ π) cos(4nx) dx x € (-x+ ²1/7) sin(4x) dx

Consider the partial differential equation 2² u du dx² Ət with boundary conditions u(0, ₺) = 0 and 1 |u(π, t) un, t) = 0 for t≥ 0, and the initial condition u(x, 0) = X u(r, t) The general solution that satisfies the boundary conditions is Select one: An Ane-16n²t Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An = = = = - = 4 7 8 T > 4 +x. TT ∞ Σ n=1 TT 1 4 1 8 4 ³/16.* π 4 4 ſ 0 1 4 1 8 4 T T π 7T 1 T) 4 IT T • (-x x X sin(4nx). X (-x + 1/7) sin(4nx) dx -x+¹) sin(4x) dx X (-x+ r) cos(4nx) dx -x+ π) cos(4nx) dx x € (-x+ ²1/7) sin(4x) dx

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 2² u du მ2 Ət with boundary conditions u(0, ₺) = 0 and 1 |u(π, t) un, t) = 0 for t≥ 0, and the initial condition u(x, 0) = X -x+ The general solution that satisfies the boundary conditions is u(r, t) Select one: Ane-16n²t sin(4nx). Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An An = = = = - = 4 2 7 8 T 4 ∞ Σ n=1 TT S 1 T 4 T 4 ſ 0 1 4 π 1 8 4 πT 1 T) 4 4 1 7T 8 4 ³/16.* π IT T • (-x x X X -x+¹) sin(4x) dx (T) (-x+ 1/7) sin(4nx) dx X -x+ r) cos(4nx) dx -x+ π) cos(4nx) dx X € (-x+ ²1/7) sin(4x) dx
Transcribed Image Text:Consider the partial differential equation 2² u du მ2 Ət with boundary conditions u(0, ₺) = 0 and 1 |u(π, t) un, t) = 0 for t≥ 0, and the initial condition u(x, 0) = X -x+ The general solution that satisfies the boundary conditions is u(r, t) Select one: Ane-16n²t sin(4nx). Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An An = = = = - = 4 2 7 8 T 4 ∞ Σ n=1 TT S 1 T 4 T 4 ſ 0 1 4 π 1 8 4 πT 1 T) 4 4 1 7T 8 4 ³/16.* π IT T • (-x x X X -x+¹) sin(4x) dx (T) (-x+ 1/7) sin(4nx) dx X -x+ r) cos(4nx) dx -x+ π) cos(4nx) dx X € (-x+ ²1/7) sin(4x) dx
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