Explanation Theorem used: Criterion for Linearly independent Solutions: Let y 1 , y 2 , … y n be n solutions of the homogenous linear nth-order differential equation on an interval I . Then, the set of solutions is linearly independent on I if and only if W ( y 1 , y 2 , … y n ) ≠ 0 for every x in the interval. Description: Let f 1 and f 2 be two linearly independent functions on an interval I

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 3, Problem 4CR

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Whether the statement, “If the set of two functions f1 and f2 are linearly independent on an interval I, then the Wronskian W(f1,f2)≠0 for all x in I” is true or false.

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Chapter 3, Problem 3CR

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Whether the statement, “If the set of two functions f 1 and f 2 are linearly independent on an interval I , then the Wronskian W ( f 1 , f 2 ) ≠ 0 for all x in I ” is true or false.

Solution Summary: The author evaluates whether the Wronskian W(f_1,y2)ne 0 for all x in I is true.

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Whether the statement, “If the set of two functions f1 and f2 are linearly independent on an interval I, then the Wronskian W(f1,f2)≠0 for all x in I” is true or false.

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Whether the statement, “If the set of two functions f 1 and f 2 are linearly independent on an interval I , then the Wronskian W ( f 1 , f 2 ) ≠ 0 for all x in I ” is true or false.

Solution Summary: The author evaluates whether the Wronskian W(f_1,y­2)ne 0 for all x in I is true.

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Whether the statement, “If the set of two functions f1 and f2 are linearly independent on an interval I, then the Wronskian W(f1,f2)≠0 for all x in I” is true or false.

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Chapter 3 Solutions

Solution Summary: The author evaluates whether the Wronskian W(f_1,y2)ne 0 for all x in I is true.