Explanation Given: The first function is given by, y 1 ( t ) = e r 1 t The second function is given by, y 2 ( t ) = e r 2 t The third function is given by, y 3 ( t ) = e r 3 t Formula used: The expression for the linearly dependent of the functions is given by, y 1 ( t ) = c 1 y 2 ( t ) + c 2 y 3 ( t ) …… ( 1 ) Calculation: Substitute e r 1 t for y 1 ( t ) , e r 2 t for y 2 ( t ) and e r 3 t for y 3 ( t ) in equation ( 1 ) . e r 1 t = c 1 e r 2 t + c 2 e r 3 t Divide the both sides of the equation by e r 2 t . e ( r 1 − r 2 ) t = c 1 + c 2 e ( r 3 − r 2 ) t Differentiate the above equation

Fundamentals of Differential Equations and Boundary Value Problems

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ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 4.2, Problem 36E

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Whether the three functions er1t, er2t and er3t are linearly independent on (−∞,∞) or not.

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Chapter 4.2, Problem 35E

Chapter 4.2, Problem 37E

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Whether the three functions e r 1 t , e r 2 t and e r 3 t are linearly independent on ( − ∞ , ∞ ) or not.

Solution Summary: The author explains that the three functions er_1t,

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To find:

Whether the three functions er1t, er2t and er3t are linearly independent on (−∞,∞) or not.

Want to see the full answer?

Chapter 4 Solutions

Whether the three functions e r 1 t , e r 2 t and e r 3 t are linearly independent on ( − ∞ , ∞ ) or not.

Solution Summary: The author explains that the three functions er_1t,

Videos

To find: Whether the three functions er1t, er2t and er3t are linearly independent on (−∞,∞) or not.

Want to see the full answer?

Chapter 4 Solutions

To find:

Whether the three functions er1t, er2t and er3t are linearly independent on (−∞,∞) or not.