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: 6

Answer

$\frac{dy}{dx}=\frac{c-x}{y}$

Work Step by Step

Differentiate in respect to $x$, using the chain rule, to get $$2x+2y\frac{dy}{dx}=2c$$ Solve for the slope of the tangent line $\frac{dy}{dx}$ to get $$2y\frac{dy}{dx}=2c-2x$$ $$\frac{dy}{dx}=\frac{c-x}{y}$$
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.