The Integrating Factor of the differential equation `(1-y^2)(dx)/(dy)+yx=a y` , `(-1ltylt1)`is
(A) `1/(y^2-1)` (B) `1/(sqrt(y^2-1))` (C) `1/(1-y^2)` (D) `1/(sqrt(1-y^2))`

Explanation

Given DE is,

`=>((1−y^2)dx)/(dy)​+yx=ay`

`⇒(dx)/(dy)​+(y​x)/(1-y^2)=(ay)/(1-y^2)​`

which is same as `(dy)/(dx)​+P(y)x=Q(y)`

Integrating factor `IF=e^(∫P(y)dy)`

`=e^(∫y/(1-y^2))​dy`

Let `t=1−y^2 `

`⇒dt=−2ydy`

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