Question

The integrating factor of the differential equation `(dy)/(dx) + y/x = x^3 −3` is ______.

Options

• log x

• e^x

• `1/x`

• x

Answer 1

The integrating factor of the differential equation `(dy)/(dx) + y/x = x^3 -3` is x.

Explanation:

The given differential equation is: 

`(dy)/(dx) + y/x = x^3 - 3`

It is in the standard linear differential equation form: 

`(dy)/(dx)` + P(x)y = Q(x)

where P(x) = `1/x`

The integrating factor (IF) is given by: 

`IF = e^(intP(x)dx) = e^(int 1/xdx) = e^ln x = x`