Question

The integrating factor of the differential equation `dy/dx+2/xy=0, x ≠0` is ______.

Options

• `2/9`

• `x^2`

• `e^(2/x)`

• `e^log (2x)`

Answer 1

The integrating factor of the differential equation `dy/dx+2/xy=0, x ≠0` is `underlinebbx^2`

Explanation:

Compare this with `dy/dx + (2y)/x = 0`

`dy/dx + Py = Q`

we get `P = 2/x` and Q = 0

Integrating factor I.F.

`= e^(intp.dx)`

`= e^(int2/x.dx)`

`= e^(2lnx)`

`= e^(lnx^2)`

I.F. = x²