The Integrating Factor of the differential equation `x(dy)/(dx)-y=2x^2`is(A) `e^(-x)` (B) `e^(-y)` (C) `1/x` (D) x

Options

A. `e^(-x)`
B. `e^(-y)`
C. `(1)/(x)`
D. `x`

Explanation

Given differential equation is : `x(dy)/(dx)-y=2x^(2)`
`implies (dy)/(dx)+(-(1)/(x))y=2x`
Comparing with the differential equation `(dy)/(dx)+Py=Q`.
`:. P=-(1)/(x)`, `Q=2x`
and `I.F.=e^(intPdx)`
`implies I.F.=e^(int(-(1)/(x))dx)impliesI.F.=e^(-log|x|)`
`implies I.F.=e^(log|-x|^(-1))=(1)/(x)` (`x gt 0` say)