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  4. Integrating factor of x (dy/dx) - y = x4 - 3x is

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Q. Integrating factor of $x \frac{dy}{dx} - y = x^4 - 3x$ is

KCETKCET 2016Differential Equations

Solution:

We have,
$x \frac{d y}{d x}-y =x^{4}-3 x $
$\Rightarrow \frac{d y}{d x}-\frac{y}{x} =x^{3}-3 $
$\therefore $ Integrating Factor (IF)$ =e^{\int \frac{-1}{x} d x} $
$=e^{-\log\, x}$
$=e^{\log \frac{1}{x}}=\frac{1}{x}$