Question

Integrating factor of the differential equation `(1 - x^2) ("d"y)/("d"x) - xy` = 1 is ______.

Options

• – x

• `x/(1 + x^2)`

• `sqrt(1 - x^2)`

• `1/2 log (1 - x^2)`

Answer 1

Integrating factor of the differential equation `(1 - x^2) ("d"y)/("d"x) - xy` = 1 is `sqrt(1 - x^2)`.

Explanation:

The given differential equation is `(1 - x^2) ("d"y)/("d"x) - xy` = 1

⇒ `("d"y)/("d"x) - x/(1 - x^2) * y = 1/(1 - x^2)`

Here, P = `x/(1 - x^2)` and Q = `1/(1 - x^2)`

∴ Integrating factor I.F. = `"e"^(int Pdx)`

= `"e"^(int (-x)/(1 - x^2) dx)`

= `"e"^(1/2 log(1 - x^2))`

= `sqrt(1 - x^2)`