Answer
(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) $\alpha'(x)= A(x)\alpha(x).$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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