   Chapter 6.1, Problem 9E

Chapter
Section
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)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 