Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 365: 114

Answer

True

Work Step by Step

$$\frac{d(Ce^x)}{dx}=Ce^x$$ So, no matter how many times we differentiate this function we get the original function back. Therefore, $$\frac{d^n(Ce^x)}{dx^n}=Ce^x$$ And hence $Ce^x$ is a solution of the equation $$\frac{d^ny}{dx^n}=y$$
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