Chapter 6.1, Problem 18E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Determining a Solution In Exercises 15–22, determine whether the function is a solution of the differential equation y ( 4 ) - 16 y = 0 .y = 2 sin x

To determine
Whether the function y=2sinx is a solution of the differential equation y(4)16y=0.

Explanation

Given:

i) The function: y=2sinx.

The differential equation: y(4)16y=0.

Explanation:

The function y=2sinx has been provided.

The following rule of differentiation has to be used:

ddx(cy)=cdydx ;c being constant.

On differentiating both sides of y with respect to x the following is derived:

y'=dydx=ddx(2sinx)=2cosx

On differentiating both sides of  y with respect to x the following is derived:

y(2)=dy'dx=ddx(2cosx)=2sinx

On differentiating both sides of y(

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