Question

The particular solution of the differential equation `"y"("dx"/"dy")` = x log x at x = e and y = 1 is ______.

Options

• xy = 2

• x = e^y

• e^xy = 2

• log x = 2y

Answer 1

The particular solution of the differential equation `"y"("dx"/"dy")` = x log x at x = e and y = 1 is x = e^y.

Explanation:

We have,

`y "dx"/"dy" = x log x`

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

On integrating both sides, we get

log y = log(logx) + log c

⇒ y = c log x

When, x = e and y = 1 ⇒ c = 1

∴ y log x

⇒ x = e^y