Chapter 6.1, Problem 9E

### 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 = ( − cos   x )   ln | sec   x +   tan   x |               y " + y = tan   x

To determine
Whether the function y=(cosx)ln|secx+tanx| is a solution for the differential equation y''+y=tanx ./p

Explanation

Given:

i) The function: y=(cosx)ln|secx+tanx|.

ii) The differential equation: y''+y=tanx ./p

Explanation:

The function y=(cosx)ln|secx+tanx| has been provided.

The product rule of differentiation has to be used on the function:

ddx(fg)=fdgdx+gdfdx ,f and g being functions of x

On differentiating both the sides of the function with respect to emx /em(using the product rule), the following is derived:

y'=dydx=ddx((cosx)ln|secx+tanx|).

=(sinx)ln|secx+tanx|cosx(secxtanx+sec2xsecx+tanx)

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