Calculus (3rd Edition)

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

Chapter 10 - Introduction to Differential Equations - 10.4 First-Order Linear Equations - Preliminary Questions - Page 523: 2


(b) $\alpha'(x)= A(x)\alpha(x).$

Work Step by Step

Since $\alpha(x)=e^{\int P(x)dx}$, then $$\alpha'(x)=P(x)e^{\int P(x)dx}=P(x)\alpha(x).$$ Then the right answer is: (b) $\alpha'(x)= A(x)\alpha(x).$
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