Discussion
The integrating factor for \( \dfrac{dy}{dx} + \dfrac{y}{x} = x \) is
Answer: C
Here \( P = 1/x \), so
\[ \mu \;=\; e^{\int (1/x)\,dx} \;=\; e^{\ln x} \;=\; x. \]
The equation becomes \( (xy)' = x^{2} \), giving \( xy = x^{3}/3 + C \). The reciprocal \( 1/x \) would come from a coefficient of \( -1/x \), so the sign of \( P \) has to be read with care
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