Question

The integrating factor of the differential equation (1 + x²)dt = (tan^-1 x - t)dx is ______.

Options

• `"e"^(tan^-1)x`

• `- "e"^((tan^(-1)x)^2/2)`

• -`"e"^(tan^-1)x`

• `"e"^((tan^(-1)x)^2/2)`

Answer 1

The integrating factor of the differential equation (1 + x²)dt = (tan^-1 x - t)dx is `underline("e"^(tan^-1)x)`.

Explanation:

(1 + x²)dt = (tan^-1 x - t)dx

`=> "dt"/"dx" + "t"/(1 + x^2) = (tan^-1 x)/(1 + x^2)`

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

`= "e"^(tan^-1)`x