Explanation The function is given as T ′ ( t ) = − λ β T ( t ) . It is known that the eigen value and eigen function for equation (5) X ″ ( x ) + λ X ( x ) = 0 , T ′ ( t ) = − λ β T ( t ) is λ n = n 2 π 2 l 2 and X n ( x ) = c n sin n π x l respectively. Now, differentiate the given equation, T ″ ( t ) = − λ β T ′ ( t ) T ″ ( t ) = − λ β ( − λ β T ( t ) ) T ″ ( t ) = λ 2 β 2 T ( t ) T ″ ( t ) − λ 2 β 2 T ( t ) = 0 The roots of above equation will be ± λ β . The general solution can be written as, T n ( t ) = A n cos β n π l t + B n sin β n π l t

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 10.2, Problem 25E

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The argument that is based on physical grounds to rule out the case where λ<0 in equation (5).

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Chapter 10.2, Problem 24E

Chapter 10.2, Problem 26E

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Chapter 10 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - Prob. 6E Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 1-8, determine all the solutions, if...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...Ch. 10.2 - In Problems 9-14, find the values of eigenvalues...

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To prove: The argument that is based on physical grounds to rule out the case where λ < 0 in equation (5).

Solution Summary: The author explains the argument that is based on physical grounds to rule out the case where lambda0 in equation (5).

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To prove:

The argument that is based on physical grounds to rule out the case where λ<0 in equation (5).

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Chapter 10 Solutions

To prove: The argument that is based on physical grounds to rule out the case where λ &lt; 0 in equation (5).

Solution Summary: The author explains the argument that is based on physical grounds to rule out the case where lambda0 in equation (5).

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To prove: The argument that is based on physical grounds to rule out the case where λ<0 in equation (5).

Want to see the full answer?

Chapter 10 Solutions

To prove: The argument that is based on physical grounds to rule out the case where λ < 0 in equation (5).

To prove:

The argument that is based on physical grounds to rule out the case where λ<0 in equation (5).