# First Order Differential Equation

#### smr101

Hi,

I don't understand the second blue line in this solution. Why is the C suddenly C' and why is it then Cx?

Thanks!

Last edited:

#### HallsofIvy

MHF Helper
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.