Question

Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.

Options

• x

• logx

• `1/x`

• – x

Answer 1

Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is `1/x`.

Explanation:

The given differential equation is `x ("d"y)/("d"x) - y = x^4 - 3x`

⇒ `("d"y)/("d"x) - y/x = x^3 - 3`

Here, P = `- 1/x` and Q = `x^3 - 3`

So, integrating factor = `"e"^(int Pdx)`

= `"e"^(int 1/x "d"x)`

= `"e"^(-logx)`

= `"e"^(log  1/x)`

= `1/x`.