Explanation Approach: If e r x , x e r x , ... , x m − 1 e r x are linearly independent on ( − ∞ , ∞ ) then there exist c 0 , c 1 , ... , c m − 1 constants such that, c 0 e r x + c 1 x e r x + ... + c m − 1 e r x x m − 1 = 0 e r x ( c 0 + c 1 x + ... + c m − 1 x m − 1 ) = 0 Because e r x ≠ 0 , this implies that c 0 + c 1 x + ... + c m − 1 x m − 1 = 0 This is a polynomial of ( m − 1 ) t h degree, c m − 1 ( x m − 1 + c m − 2 c m − 1 +

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 6.2, Problem 25E

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The m functions erx,xerx,...,xm−1erx are linearly independent on (−∞,∞).

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Chapter 6.2, Problem 24E

Chapter 6.2, Problem 26E

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Chapter 6 Solutions

Fundamentals of Differential Equations and Boundary Value Problems

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The m functions e r x , x e r x , ... , x m − 1 e r x are linearly independent on ( − ∞ , ∞ ) .

Solution Summary: The author explains that the m functions erx,mathrm...

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To show:

The m functions erx,xerx,...,xm−1erx are linearly independent on (−∞,∞).

Want to see the full answer?

Chapter 6 Solutions

The m functions e r x , x e r x , ... , x m − 1 e r x are linearly independent on ( − ∞ , ∞ ) .

Solution Summary: The author explains that the m functions erx,mathrm...

Videos

To show: The m functions erx,xerx,...,xm−1erx are linearly independent on (−∞,∞).

Want to see the full answer?

Chapter 6 Solutions

To show:

The m functions erx,xerx,...,xm−1erx are linearly independent on (−∞,∞).