Question

The integrating factor of the differential equation 2x`dy/dx` – y = 3 is ______.

Options

• `sqrtx`

• `sqrt1/x`

• e^x

• e^–x

Answer 1

The integrating factor of the differential equation 2x`dy/dx` – y = 3 is `bbunderline(sqrt1/x)`.

Explanation:

2x`dy/dx` – y = 3

`dy/dx-y/(2x)=3/(2x)`

`dy/dx-1/(2x)y=3/(2x)`

P(x) = `-1/(2x)`

I.F. = `e^(f-1/(2x)dx)`

= `e^(-1/2f1/xdx)`

= `e^(-1/2In  x)`

= `e^(Inx^(-1/2)`

= `x^(-1/2)`

= `1/sqrtx`