i wont write the whole question, but the term

$\displaystyle \frac{dy}{dx} \times \frac{1}{y}$

in the next line they change to

$\displaystyle \frac{d (ln(y))}{dx}$

i just dont see why you would be able to do that. none of the other terms in the equation (i havent written out) are changed. only thing i can think of is some sort of implicit differentiation idea or some sort. im not too sure