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

Explanation

D Is Correct Answer



`frac{d x}{d y}+frac{y x}{1-y^{2}}=frac{a y}{1-y^{2}} `


`P=frac{y}{1-y^{2}}, Q=frac{a y}{1-y^{2}} `


`I . F=int frac{y}{1-y^{2}} d y `


`=e^{-frac{1}{2} int frac{-2 y}{1-y^{2}} d y}=e^{-frac{1}{2} log (1-y^{2})} `


`e^{log frac{1}{sqrt{1-y^{2}}}=} frac{1}{sqrt{1-y^{2}}} `