Elementary Differential Equations and Boundary Value Problems 9th Edition

Published by Wiley
ISBN 10: 0-47038-334-8
ISBN 13: 978-0-47038-334-6

Chapter 1 - Introduction - 1.3 Classification of Differential Equations - Problems - Page 24: 3


The order is 4. It is linear.

Work Step by Step

The differential equation $$\frac{d^4y}{dt^4} +\frac{d^3y}{dt^3}+\frac{d^2y}{dt^2} +\frac{dy}{dt}+y=1 $$ has order 4 because the fourth derivative $\frac{d^4y}{dt^4}$ is the highest derivative in the equation. To see it is linear, we subtract $1$ from both sides to get $$\frac{d^4y}{dt^4} +\frac{d^3y}{dt^3}+\frac{d^2y}{dt^2} +\frac{dy}{dt}+y-1=0.$$ Since the left hand side is a linear function of $y$ and its derivatives, our original differential equation is linear.
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