Question

Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` . 

Answer 1

`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`