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Integrating Factor

I.F. of x+1...

Question

I.F. of $(x + 1) \frac{d y}{d x} - y = e^{2 x} (x + 1)$ is:

A

log (x + 1)

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B

\frac{e^{2 x}}{2}

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C

- (x + 1)

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D

\frac{1}{x + 1}

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Solution

The correct option is C $\frac{1}{x + 1}$
$\frac{d y}{d x} - \frac{y}{x + 1} = e^{2 x} (x + 1)$
$I . F = e^{\int P (x) d x} = e^{- \int \frac{1}{x + 1} d x} = e^{- log (x + 1)} = \frac{1}{x + 1}$

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