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The integrating factor of the differential equation $x \frac{d y}{d x}-y=\sin x$ is: |
$-\frac{1}{x}$ $x$ $e^{\log x}$ $\frac{1}{x}$ |
$\frac{1}{x}$ |
The correct answer is Option (4) → $\frac{1}{x}$ $x \frac{d y}{d x}-y=\sin x$ $⇒\frac{d y}{d x}-\frac{1}{x}=\frac{\sin x}{x}$ I.F. = $e^{\int P(x)dx}e^{-\int\frac{1}{x}dx}=e^{\log_e(\frac{1}{x})}=\frac{1}{x}$ |
