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Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

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Section
BuyFindarrow_forward

Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378
Chapter 16.3, Problem 24E
Textbook Problem
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Method of Variation of Parameters In Exercises 23–28, solve the differential equation by the method of variation of parameters.

y ' ' + y = sec x tan x

To determine

To calculate: The solution of the given differential equation y''+y=secxtanx by the method of variation of parameters.

Explanation of Solution

Given information:

The given differential equation is y''+y=secxtanx.

Concept Used:

To find the general solution of the equation y''+ay'+by=F(x) use the below steps.

Find yh=C1y1+C2y2.

Replace the constants by variables to form yp=u1y1+u2y2.

Solve the following system for u1' and u2'.

u1'y1+u2'y2=0u1'y1'+u2'y2'=F(x)

Integrate to find u1 and u2. The general solution is y=yh+yp.

Calculation:

The characteristics equation is m2+1=0.

First, we have to find the solution of the characteristics equation m2+1=0.

m2+1=0m2=1m=±im=iorm=i

Therefore,

yh=C1cosx+C2sinx

Replacing C1 and C2 by u1 and u2 gives yp=u1cosx+u2sinx

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Chapter 16 Solutions

Multivariable Calculus
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