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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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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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