Chapter 10 - Introduction to Differential Equations - 10.4 First-Order Linear Equations - Preliminary Questions - Page 523: 3

$$P(x)=\frac{1}{x}.$$

Work Step by Step

Since $\alpha(x)=e^{\int P(x)dx}$, then $$e^{\int P(x)dx}=x\Longrightarrow \int P(x)dx = \ln x.$$ Hence, by differentiation, we have $$P(x)=\frac{1}{x}.$$

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