If \(\displaystyle ln|y|= \frac{-1}{x}+C'\) then getting comm-on denominators and adding the fractions on the right,

\(\displaystyle ln|y|=-\frac{1}{x}+ \frac{C'x}{x}= \frac{C'x- 1}{x}\)

C doesn't become C', C' becomes C! And I suspect the initial ' was a typo.