## Calculus (3rd Edition)

Published by W. H. Freeman

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

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

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