Question

The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is ______.

Options

• e^-x

• e^-y

• `1/x`

• x

Answer 1

The Integrating Factor of the differential equation `dy/dx - y = 2x^2` is `underline(1/x)`

Explanation:

The differential equation is

`x dy/dx - y = 2x^2`

or `dy/dx - 1/x y = 2x`

Here `P = - 1/x, Q = 2x`

∴ `∫ P  dx =int - 1/x` dx

=` - log x = log  1/x`

⇒ `I.F. = e^(int P dx)`

`= e^(log 1//x) = 1/x`