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: 9


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Work Step by Step

Differentiate the equation in respect to $x$. $$x^2+y^2=c$$ $$2x+2y \times y'=0$$ Solve for $y'$. $$y \times y'=-x$$ $$y'=-\frac{x}{y}$$ This expression matches the given differential equation $y'=-x/y$ exactly, therefore, the equation is a solution.
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