integrate dydx=(4sqrt(y)lnx)/x.

Check my answer? I got y=((2ln^2(x)+c)/2)^2. Is that right?

3 answers

Take your answer, and take the derivative.
y=((2ln^2(x)+c)/2)^2
y'=2(sqrty)(4lnx/2)
Yep, looks right
I assume

dy/dx=(4sqrt(y)ln x)/x

y^-.5 dy = 4 (ln x /x)dx

y^.5 = 2 [ .5 ln^2 x ]

y^.5 = ln^2 x

y = ln^4 x + c
Yes we agree but I simplified