Explanation Given: The differential equation is, ( y 3 + k x y 4 − 2 x ) d x + ( 3 x y 2 + 20 x 2 y 3 ) d y = 0 Procedure used: Compare the given differential equation with the standard form of exact differential equation M d x + N d y = 0 . To check whether the given differential equation is exact or not, check the condition ∂ M ∂ y = ∂ N ∂ x is satisfied or not. Calculation: Compare the given differential equation with the standard form of exact differential equation. Thus, M = ( y 3 + k x y 4 − 2 x ) and N = ( 3 x y 2 + 20 x 2 y 3 ) . Calculate ∂ M ∂ y as follows. ∂ M ∂ y = ∂ ∂ y ( y 3 + k x y 4 − 2 x ) = 3 y 2 + 4 k x y 3 Calculate ∂ N ∂ x as follows

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 2.4, Problem 27E

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Find the value of k so that the given differential equation is exact.

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Chapter 2.4, Problem 26E

Chapter 2.4, Problem 28E

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Advanced Engineering Mathematics

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Chapter 2 Solutions