Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 10 - Introduction to Differential Equations - 10.3 The Logistic Equation - Preliminary Questions - Page 518: 2


It is not linear.

Work Step by Step

The logistic differential equation is of the form $$ \frac{d y}{d t}=k y\left(1-\frac{y}{A}\right) =ky-\frac{ky^2}{A}$$ which is not of the form of a linear differential equation (notice the $y^2$ term). Thus, it is not linear.
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