Explanation Given: i) The function is y = 3 cos 2 x . The differential equation is y ( 4 ) − 16 y = 0 . Explanation: The function y = 3 cos 2 x has been provided. Following rule of differentiation has to be used: d d x ( c y ) = c d y d x ; c being a constant. On differentiating both sides of y with respect to x , the following is derived: y ' = d y d x = d d x ( 3 cos 2 x ) = − 6 sin 2 x On differentiating both sides of y ' with respect to x the following is derived: y ( 2 ) = d y ' d x = d d x ( − 6 sin 2 x ) = − 12 cos 2 x On differentiating both sides of y ( 2 )

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 6.1, Problem 15E

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Whether the function y=3cos2x is a solution of the differential equation y(4)−16y=0.

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Chapter 6.1, Problem 14E

Chapter 6.1, Problem 16E

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Whether the function y = 3 cos 2 x is a solution of the differential equation y ( 4 ) − 16 y = 0 .

Solution Summary: The author explains that the function y=3mathrmcos2x is a solution of the differential equation

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Whether the function y=3cos2x is a solution of the differential equation y(4)−16y=0.

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