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 - 1.1 Differential Equations Everywhere - Problems - Page 12: 21



Work Step by Step

given that $x^2+y^2=2cx$ $c=\frac{x^2+y^2}{2x}$ differentiate the above term with respect to x $2x+2y\frac{dy}{dx}=2c$ $\frac{dy}{dx}=\frac{c-x}{y}$ $\frac{dy}{dx}=\frac{\frac{x^2+y^2}{2x}-x}{y}$ $\frac{dy}{dx}=\frac{y^2-x^2}{2xy}$ for orthogonal trajectory $\frac{dy}{dx}=\frac{-1}{f(x,y)}$ $\frac{dy}{dx}=\frac{2xy}{x^2-y^2}$ thus,the final answer $\frac{dy}{dx}=\frac{2xy}{x^2-y^2}$
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