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 - 1.4 Separable Differential Equations - True-False Review: i

Answer

True.

Work Step by Step

Factor out the expression on the right to get $$\frac{dy}{dx}=\frac{xy(x^2+xy)}{x^2+xy}=xy$$ $$\frac{dy}{dx}=xy$$ Multiplying the equation by $\frac{dx}{y}$ yields $$\frac{dy}{y}=xdx$$ Therefore, the variables can be separated and the equation must be separable.
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