alleryThe integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2$ is:
A$x$
B$\log x$
C$x^2$
D$e^x$
Answer & Solution
Correct answer: A. $x$
Comparing with $\dfrac{dy}{dx} + P y = Q$ gives $P = 1/x$.
**Hence $\text{IF} = e^{\int P\,dx} = e^{\int (1/x)\,dx} = e^{\log x} = x$.**
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