Explanation Given: The given differential equation is d y d x = sin ( x + y ) . Procedure used: Use the following substitution in the given differential equation: u = ( x + y ) Differentiate the substitution equation with respect to x . d u d x = d ( x + y ) d x d u d x = d ( x ) d x + d ( y ) d x d u d x = 1 + d y d x d y d x = d u d x − 1 Calculation: Substitute d u d x − 1 for d y d x and u for ( x + y ) in the given differential equation. d u d x − 1 = sin u d u d x = sin u + 1 d u sin u + 1 = d x (1) Multiply the left-hand side of the equation (1) with 1 − sin u 1 − sin u

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 26E

To determine

The solution of the given differential equation by using an appropriate substitution.

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Chapter 2.5, Problem 25E

Chapter 2.5, Problem 27E

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Chapter 2 Solutions

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The solution of the given differential equation by using an appropriate substitution.

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Chapter 2 Solutions