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Consider the partial differential equation 2² u du მე2 Ət 1 with boundary conditions u(0, t) = 0 and u(π, t) = 0 for ₺ ≥ 0, and the initial condition u(x,0) = x x The general solution that satisfies the boundary conditions is Select one: ∞ u(x, t) = Σ Ane¯4n²³ t Σ₁ n=1 An An Select the option that gives the correct method for determining the constants An from the given initial condition. An An An - || || || > = 4 π 1 2 2 [ ³* x (x − ² 7) cos(2nx) dx πT 2 π 1 s - 12/₁7). 2 --T ko me to T sin(2nx). 7T x (x − ½-r) sin(2nx) dx 1 T 2 [ ³* x (x − ½r) sin(2nx) dx π 1 T 2 [*³* 0 x (x − ²½ r) sin(2nx) dr 1 4 2 [ ³* x (x − ²½ 7) cos(2nx) da 2 7T

Consider the partial differential equation 2² u du მე2 Ət 1 with boundary conditions u(0, t) = 0 and u(π, t) = 0 for ₺ ≥ 0, and the initial condition u(x,0) = x x The general solution that satisfies the boundary conditions is Select one: ∞ u(x, t) = Σ Ane¯4n²³ t Σ₁ n=1 An An Select the option that gives the correct method for determining the constants An from the given initial condition. An An An - || || || > = 4 π 1 2 2 [ ³* x (x − ² 7) cos(2nx) dx πT 2 π 1 s - 12/₁7). 2 --T ko me to T sin(2nx). 7T x (x − ½-r) sin(2nx) dx 1 T 2 [ ³* x (x − ½r) sin(2nx) dx π 1 T 2 [*³* 0 x (x − ²½ r) sin(2nx) dr 1 4 2 [ ³* x (x − ²½ 7) cos(2nx) da 2 7T

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 მე2 Ət 1 with boundary conditions u(0, t) = 0 and u(π, t) = 0 for ₺ ≥ 0, and the initial condition u(x,0) = x x --T -1/2). The general solution that satisfies the boundary conditions is ∞ u(x, t) = Σ Ane¯4n²³ t Σ₁ n=1 Select one: Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An An - || || || > = 4 1 2 2 [ ³* x (x − ² 7) cos(2nx) dx πT π 2 π 1 2 s 1 sin(2nx). 2 1 2 [ ³* x (x − ½r) sin(2nx) dx π x (x − ²/7) sin(2nx) dx T 1 T 2 [³* x (x − ²½ r) sin(2nx) dr 1 4 2 [ ³* x (x − ¾ ñ) cos(2nx) dz 2 7T 0
Transcribed Image Text:Consider the partial differential equation 2² u du მე2 Ət 1 with boundary conditions u(0, t) = 0 and u(π, t) = 0 for ₺ ≥ 0, and the initial condition u(x,0) = x x --T -1/2). The general solution that satisfies the boundary conditions is ∞ u(x, t) = Σ Ane¯4n²³ t Σ₁ n=1 Select one: Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An An - || || || > = 4 1 2 2 [ ³* x (x − ² 7) cos(2nx) dx πT π 2 π 1 2 s 1 sin(2nx). 2 1 2 [ ³* x (x − ½r) sin(2nx) dx π x (x − ²/7) sin(2nx) dx T 1 T 2 [³* x (x − ²½ r) sin(2nx) dr 1 4 2 [ ³* x (x − ¾ ñ) cos(2nx) dz 2 7T 0
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