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The integrating factor for the linear DE $\dfrac{dy}{dx} + P(x)y = Q(x)$ is:
A$\int P\,dx$
B$e^{\int P\,dx}$
C$e^{-\int P\,dx}$
D$e^{Q}$
Answer & Solution
Correct answer: B. $e^{\int P\,dx}$
Multiplying by $\mu = e^{\int P\,dx}$ turns the LHS into $\dfrac{d}{dx}(\mu y)$. Then integrate both sides: $\mu y = \int Q\mu\,dx + c$.
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