Question

The integrating factor of the differential equation x`"dy"/"dx"` + y log x = x² is ______.

Options

• `x^(logsqrtx)`

• (log x)²

• `x^(log x)`

• (log x)^x

Answer 1

The integrating factor of the differential equation x`"dy"/"dx"` + y log x = x² is `underline(x^(logsqrtx))`.

Explanation:

We have,

x`"dy"/"dx"` + y log x = x² 

`"dy"/"dx" + y((log x)/x)` = x

IF = `e^(int ((log x)/x)"dx")`

`= e^((log x)^2/2)`

`= e^(1/2 log x * log x)`

`= e^(log sqrtx log x)`

`= e^(log x log sqrtx)`

= `x^(log sqrtx)`