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Find the Integerating Factor of the Differential Equation X D Y D X − 2 Y = 2 X 2 - Mathematics

Sum

Find the integerating factor of the differential equation `x(dy)/(dx) - 2y = 2x^2`

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Solution

`(dy)/(dx) + (-2/x)y = 2x`

compare with `(dy)/(dx) + py = Q`

⇒ `p = -2/x`

`therefore` Integrating factor `IF = e^(∫pdx)`

= `e^(∫-2/xdx)`

= `e^(-2  "In"  x)`

= `e^("In"  x^-2)`

= `x^-2`

= `1/x^2`

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