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 - True-False Review: b

Answer

False.

Work Step by Step

For a differential equation $\frac{dy}{dx}=f(x,y)$ to have an equilibrium solution, the function $f(x,y)$ must equal zero, or have a solution. Therefore, if the function $f(x,y)$ equals $x^2+4$, which has no real solution, there is no equilibrium solution.
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