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 - 1.2 Basic Ideas and Terminology - Problems: 31

Answer

$\frac{dy}{dx} = \frac{x^{2}(1 - y^{2}) + ye^{\frac{y}{x}}}{x(e^{\frac{x}{y}} + 2x^{2}y)}$

Work Step by Step

$e^{\frac{x}{y}} + xy^{2} - x = c$ Implicit differentiation: differentiating the equation in terms of $x$: $e^{\frac{y}{x}}\frac{x\frac{dy}{dx} - y}{x^{2}} + 2xy\frac{dy}{dx} + y^{2} - 1 = 0$ Express the equation in terms of $\frac{dy}{dx}$; $\frac{dy}{dx} = \frac{x^{2}(1 - y^{2}) + ye^{\frac{y}{x}}}{x(e^{\frac{x}{y}} + 2x^{2}y)}$
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