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 - 1.2 Basic Ideas and Terminology - Problems - Page 22: 45

Answer

See below.

Work Step by Step

Take the derivatives of the function. $$y(x)=c_1e^{2x}+c_2e^{-3x}$$ $$y'(x)=2c_1e^{2x}-3c_2e^{-3x}$$ $$y''(x)=4c_1e^{2x}+9c^2e^{-3x}$$ Substituting these functions into the differential equation yields $$y''+y'-6y=0$$ $$4c_1e^{2x}+9c^2e^{-3x}+2c_1e^{2x}-3c_2e^{-3x}-6(c_1e^{2x}+c_2e^{-3x})=0$$ $$0=0$$ This statement is true, therefore, the equation must be a valid solution to the differential equation.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.