Explanation Result used: Wronskian of two functions: “If the functions y 1 and y 2 are linearly dependent, then the columns of the Wronskian as differentiation is a linear operation, that is, W ( y 1 , y 2 ) = 0 . If W ( y 1 , y 2 ) ≠ 0 , then the functions y 1 and y 2 are linearly independent. The Wronskian of two functions is compute as follows. W ( y 1 , y 2 ) = | y 1 y 2 y 1 ′ y 2 ′ | = y 1 y 2 ′ − y 2 y 1 ′ ”. Calculation: Let y 1 = ln x , and y 2 = ln ( x 3 ) . Compute the derivative of y 1 as follows. y 1 ′ = 1 x Compute the derivative of y 2 as follows. y 2 ′ = d d x ln ( x 3 ) = d d u ln ( u ) ⋅ d d x ( x 3 ) [

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ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Chapter 2.2, Problem 34P

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To check: Whether the given functions are linearly independent.

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Chapter 2.2, Problem 33P

Chapter 2.2, Problem 35P

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