Question

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

Options

• x

• `x/((1 + x^2))`

• (1 + x²)

• log (1 + x²)

Answer 1

An integrating factor of the differential equation `(1 + x^2) ("d"y)/("d"x) + 2xy` = 1  is (1 + x²).

Explanation:

`(1 + x^2) ("d"y)/("d"x) + 2xy` = 1

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

∴ I.F. = `"e"^(int (2x)/(1 + x^2) "d"x)`

= `"e"^(log(1 + x^2)`

= (1 + x²)