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azu = a ax2 ди 5. A partial differential equation is where a is a given constant and a>0,00. at The boundary conditions for the equation are u(0,1)=0 and u(L,t)=0 . The initial condition is u(x, 0) = b, where b is a given constant. (1) Use the method of separation of variables to transform the partial differential equation into ordinary differential equations. You must use the following notations: u(x, t) = f(x)g(t) (2) Derive the boundary conditions for function f (x). (3) Obtain the solutions for f(x). (4) Obtain a solution for u(x, t) such that the initial condition u(x,0) = b is satisfied.

azu = a ax2 ди 5. A partial differential equation is where a is a given constant and a>0,00. at The boundary conditions for the equation are u(0,1)=0 and u(L,t)=0 . The initial condition is u(x, 0) = b, where b is a given constant. (1) Use the method of separation of variables to transform the partial differential equation into ordinary differential equations. You must use the following notations: u(x, t) = f(x)g(t) (2) Derive the boundary conditions for function f (x). (3) Obtain the solutions for f(x). (4) Obtain a solution for u(x, t) such that the initial condition u(x,0) = b is satisfied.

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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azu = a ax2 ди 5. A partial differential equation is where a is a given constant and a>0,0<x<L, and t>0. at The boundary conditions for the equation are u(0,1)=0 and u(L,t)=0 . The initial condition is u(x, 0) = b, where b is a given constant. (1) Use the method of separation of variables to transform the partial differential equation into ordinary differential equations. You must use the following notations: u(x, t) = f(x)g(t) (2) Derive the boundary conditions for function f (x). (3) Obtain the solutions for f(x). (4) Obtain a solution for u(x, t) such that the initial condition u(x,0) = b is satisfied.
Transcribed Image Text:azu = a ax2 ди 5. A partial differential equation is where a is a given constant and a>0,0<x<L, and t>0. at The boundary conditions for the equation are u(0,1)=0 and u(L,t)=0 . The initial condition is u(x, 0) = b, where b is a given constant. (1) Use the method of separation of variables to transform the partial differential equation into ordinary differential equations. You must use the following notations: u(x, t) = f(x)g(t) (2) Derive the boundary conditions for function f (x). (3) Obtain the solutions for f(x). (4) Obtain a solution for u(x, t) such that the initial condition u(x,0) = b is satisfied.
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