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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The integrating factor for solving the differential equation $x \frac{d y}{d x}-y=2 x^2$ is
  • A
    $e^{-y}$
  • B
    $e^{-e}$
  • C
    $x$
  • ✓
    $\frac{1}{x}$
✓

Answer

Correct option: D.
$\frac{1}{x}$
(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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