Explanation Given information: The given function are y 1 = e a x sin b x and y 2 = e a x cos b x . Concept Used: The Wronskian of two differentiable functions f and g , denoted by W (f, g) , is defined as the function given by the determinant W ( f , g ) = | f g f ' g ' | . Proof: First, find the derivative of the y 1 and y 2 with respect to x , we get y 1 ' = b e a x c o s b x + a e a x sin b x and y 2 ' = a e a x cos b x − b e a x sin b x Now, we have to find the determinant W ( y 1 , y 2 ) = | y 1 y 2 y 1 ' y 2 ' | . W ( y 1 , y 2 ) = | e a x sin b x e a x cos b x b e a x c o s b x + a e a x sin b x

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ISBN: 9781337604796

Author: Larson

Publisher: CENGAGE L

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Chapter 16.2, Problem 73E

To determine

To verify:

The two function y1=eaxsinbx and y2=eaxcosbx are linearly independent by using Wronskian Method.

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Chapter 16.2, Problem 72E

Chapter 16.2, Problem 74E

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To verify: The two function y 1 = e a x sin b x and y 2 = e a x cos b x are linearly independent by using Wronskian Method.

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To verify: The two function y1=eaxsinbx and y2=eaxcosbx are linearly independent by using Wronskian Method.

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Chapter 16 Solutions

To verify:

The two function y1=eaxsinbx and y2=eaxcosbx are linearly independent by using Wronskian Method.