Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 1 - First-Order Differential Equations - 1.3 The Geometry of First-Order Differential Equations - Problems: 9

Answer

See below.

Work Step by Step

Differentiate the equation in respect to $x$. $$x^2+y^2=c$$ $$2x+2y \times y'=0$$ Solve for $y'$. $$y \times y'=-x$$ $$y'=-\frac{x}{y}$$ This expression matches the given differential equation $y'=-x/y$ exactly, therefore, the equation is a solution.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.