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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 `xdy/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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