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: 7

Answer

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

Work Step by Step

Differentiate in respect to $x$, remembering to use chain rule. $$2(x-c)+2(y-c)\frac{dy}{dx}=0$$ Solve for the slope of the tangent line $\frac{dy}{dx}$ to get $$2(y-c)\frac{dy}{dx}=-2(x-c)$$ $$\frac{dy}{dx}=\frac{-(x-c)}{y-c}$$ $$\frac{dy}{dx}=\frac{c-x}{y-c}$$
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