First Order Differential Equation

Sep 2012
66
0
Scotland
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
Apr 2005
20,249
7,909
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.