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Differential Equations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDifferential Equations1 Mark
Question
The integrating factor for solving the differential equation $x \frac{d y}{d x}-y=2 x^2$ is
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Answer

(d) : We have, $x \frac{d y}{d x}-y=2 x^2$
i.e., $\frac{d y}{d x}-\frac{y}{x}=2 x \quad \therefore \quad$ I.F. $=e^{\int \frac{-1}{x} d x}=e^{-\ln x}=e^{\ln x^{-1}}=\frac{1}{x}$
$\therefore$ Integrating factor is $\frac{1}{x}$.

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