Chapter 6.1, Problem 7E

### 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

# Verifying a Solution In Exercises 5–10, verify that the function is a solution of the differential equation.Function Differential Equation y = C 1   sin   x −   C 2   cos   x               y " + y = 0

To determine
Whether the function y=C1sinxC2cosx is a solution for the differential equation y''+y=0.

Explanation

Given:

i) The function: y=C1sinxC2cosx.

ii) The differential equation: y''+y=0.

Explanation:

A function y=C1sinxC2cosx has been provided.

The rule of differentiation to be used on the function is as follows:

ddx(cy)=cdydx , c being constant

On differentiating both the sides of the function with respect to emx/em, the following is derived:

y'=dydx=ddx(C1sinxC2cosx)=C1ddx(sinx)C2ddx(cosx)=C1cosx+C2sinx

On differentiating <

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