Explanation Given information: The given initial value problem is, x 2 d y d x = y − x y y ( − 1 ) = − 1 Definition used: “A solution in which the dependent variable is expressed solely in terms of the independent variable and constant is said to be an explicit solution.” Calculation: Consider the differential equation. x 2 d y d x = y − x y Rewrite the differential equation in the form as. x 2 d y d x = y ( 1 − x ) d y y = ( 1 − x ) x 2 d x d y y = ( 1 x 2 − 1 x ) d x Integrate on both sides of the equation. ∫ d y y = ∫ ( 1 x 2 − 1 x ) d x ∫ d y y = ∫ 1 x 2 d x − ∫ 1 x d x ln | y | = − 1 x − ln | x | + C ln | y | + ln | x | = C − 1 x Simplify further

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Question

Chapter 2.2, Problem 25E

To determine

The explicit solution of the given initial value problem.

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Chapter 2.2, Problem 24E

Chapter 2.2, Problem 26E

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Chapter 2 Solutions

Advanced Engineering Mathematics

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