,y(e) = 0

It is a homogeneous equation

Put y = vx

And

So,

On integrating both sides,

log xc

v = log(log xc)

put value of v,

log(log x) + k ……(1)

Put y = 0, x = e

0 = e log(log e) + k

k = 0

put in eq. (1),

y = x log(log(x))