(i) If a differential equation is ,

then y(I.F) = ∫Q.(I.F)dx + c, where I.F = e^∫Pdx

Given:-

This is a linear differential equation, comparing it with

Q = log x

I.F = e^∫Pdx

= e^log|x|

= x, x>0

The solution of the equation is given by

y(I.F) = ∫Q.(I.F)dx + c

⇒ yx = ∫logx.x.dx + c