Question

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

Answer 1

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

Explanation:

Given that

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

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

This differential equation is of the form

`dy/dx + Py = Q`

P = `2/x` and Q = x

I.F. = `e^(int 2/x dx)`

= `e^(logx^2)`

= x²