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: f

Answer

True.

Work Step by Step

Using exponent rules, $e^{x+y}$ can be changed to $e^xe^y$. This changes the equation to $$\frac{dy}{dx}=e^xe^y$$ The variables can be separated by multiplying the entire equation by $\frac{dx}{e^y}$. $$\frac{dy}{e^y}=e^xdx$$ Therefore, the equation is separable.
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