Explanation Given: The first function is given by, y 1 ( t ) = t e 2 t …… ( 1 ) The second function is given by, y 2 ( t ) = e 2 t …… ( 2 ) The interval in which the linear dependency is to be checked is ( 0 , 1 ) . Approach: If one function is the constant multiple of another in a certain interval then both functions will be linearly dependent to each other in that particular interval. The relation between the function which are linearly dependent is, y 1 ( t ) = k y 2 ( t ) …… ( 3 ) Here, the constant is k . Calculation: Rewrite the equation ( 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 4.2, Problem 29E

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Whether the functions y1 and y2 are linearly dependent on the interval (0,1) or linearly independent.

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Chapter 4.2, Problem 28E

Chapter 4.2, Problem 30E

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Whether the functions y 1 and y 2 are linearly dependent on the interval ( 0 , 1 ) or linearly independent.

Solution Summary: The author explains that if one function is the constant multiple of another in a certain interval then both functions are linearly dependent to each other in that particular interval.

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To find:

Whether the functions y1 and y2 are linearly dependent on the interval (0,1) or linearly independent.

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Chapter 4 Solutions

Whether the functions y 1 and y 2 are linearly dependent on the interval ( 0 , 1 ) or linearly independent.

Solution Summary: The author explains that if one function is the constant multiple of another in a certain interval then both functions are linearly dependent to each other in that particular interval.

Concept explainers

Videos

To find: Whether the functions y1 and y2 are linearly dependent on the interval (0,1) or linearly independent.

Want to see the full answer?

Chapter 4 Solutions

To find:

Whether the functions y1 and y2 are linearly dependent on the interval (0,1) or linearly independent.