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Find the solution u (x,t) to the partial differential equation using the method of separation of variables: ди = a at with boundary conditions u (x =- L,t) u (x=+ L,t), ди (x=- L,t) ди (x=+L,t), and an initial condition u (x,t =0) = f (x), where f(x) is a given function of x. Hint: consider the separation constant (-A), for A>0 and X=0.

Find the solution u (x,t) to the partial differential equation using the method of separation of variables: ди = a at with boundary conditions u (x =- L,t) u (x=+ L,t), ди (x=- L,t) ди (x=+L,t), and an initial condition u (x,t =0) = f (x), where f(x) is a given function of x. Hint: consider the separation constant (-A), for A>0 and X=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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Find the solution u (x,t) to the partial differential equation using the method of separation of variables: ди = a at with boundary conditions u (x =- L,t) u (x=+ L,t), ди (x=- L,t) ди (x=+L,t), and an initial condition u (x,t =0) = f (x), where f(x) is a given function of x. Hint: consider the separation constant (-A), for A>0 and X=0.
Transcribed Image Text:Find the solution u (x,t) to the partial differential equation using the method of separation of variables: ди = a at with boundary conditions u (x =- L,t) u (x=+ L,t), ди (x=- L,t) ди (x=+L,t), and an initial condition u (x,t =0) = f (x), where f(x) is a given function of x. Hint: consider the separation constant (-A), for A>0 and X=0.
Find the solution u (x,t) to the partial differential equation using the method of separation of variables: ди = a at with boundary conditions u (x =- L,t) u (x=+ L,t), ди (x=- L,t) ди (x=+L,t), and an initial condition u (x,t =0) = f (x), where f(x) is a given function of x. Hint: consider the separation constant (-A), for A>0 and X=0.
Transcribed Image Text:Find the solution u (x,t) to the partial differential equation using the method of separation of variables: ди = a at with boundary conditions u (x =- L,t) u (x=+ L,t), ди (x=- L,t) ди (x=+L,t), and an initial condition u (x,t =0) = f (x), where f(x) is a given function of x. Hint: consider the separation constant (-A), for A>0 and X=0.
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