Explanation Given: The given differential equation is x y ′ = y ln ( x y ) . Calculation: Consider the given differential equation, x y ′ = y ln ( x y ) (1) Consider the equation, u = ln y Differentiate the equation with respect to x . d u d x = 1 x ( ln x + u ) d u d x − 1 x u = ln x x (2) Equation (2) is the linear equation of the form, d u d x + P ( x ) u = Q ( x ) (3) Solution of above the linear form is, u × I . F = ∫ ( Q ( x ) × I . F ) d x (4) Compare equation (2) and equation (3), P ( x ) = − 1 x Q ( x ) = ln x x Integrating factor is, I . F = e ∫ P ( x ) d x (5) Substitute − 1 x for P ( x ) in equation (5). I . F = e ∫ − 1 x d x = e ln ( x ) − 1 = 1 x Substitute 1 x for I

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 2.5, Problem 36E

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The solution of the given differential equation.

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Chapter 2.5, Problem 35E

Chapter 2.5, Problem 37E

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1. Name the ongiewing) 2. Name five pairs of supple 3 27 and 19 form a angles 210 and 21 are complementary angies 4. m210=32 mal!= 5 mc11-72 m10= 6 m210-4x mc11=2x x= 7 m210=x m 11 =x+20; x= 12 and 213 are supplementary angles 8 ma 12 2y m13-3y-15 y= 9 m 12-y+10 m13-3y+ 10: y= 10. The measure of 212 is five times the measure of 13. Find the 213 and 214 are complementary angles, and 14 and 15 are supplementary angies 11 mc13 47 m/14- 12 m 14-78 m13- m215- m15 13 m15-135 m. 13- m.14

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Chapter 2 Solutions

Advanced Engineering Mathematics

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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The solution of the given differential equation.

Solution Summary: The author explains the solution of the given differential equation, which is y=ecx-1x

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Chapter 2 Solutions