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 - Page 32: 6



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 $$2y\frac{dy}{dx}=2c-2x$$ $$\frac{dy}{dx}=\frac{c-x}{y}$$
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