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  4. The integrating factor of the differential equation x ( dy / dx )- y =2 x 2 is

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Q. The integrating factor of the differential equation $x \frac{ dy }{ dx }- y =2 x ^{2} is$

Differential Equations

Solution:

$x \frac{ dy }{ dx }- y =2 x ^{2}$ or
$\frac{ dy }{ dx }-\frac{ y }{ x }=2 x$
$I . F = e ^{\int \frac{-1}{ x } dx }= e ^{-\log x }$
$= e ^{\log \frac{1}{ x }}=\frac{1}{ x }$