Question

The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is ______.

विकल्प

• `1/"x"`

• k

• `1/"n"^2`

• x²

• x

• `1/x^2`

Answer 1

The integrating factor of linear differential equation `x dy/dx + 2y = x^2 log x` is x².

Explanation:

`x dy/dx + 2y = x^2 log x`

⇒ `dy/dx + (2/x)y = x log x`

This is Linear differential equation of the form

`dy/dx + P = Q`

where `P = 2/x`

∴ Integrating factor (I. F.) = `e^(int pdx)`

`e^(int 2/x dx)`

= `e^(2 log x)`

`e^(logx^2)`

= x²