I'm trying to find the general solution for
$(x+2)y' = 3-\frac{2y}{x}$
This is what I've done so far:
$y'+\frac{2y}{x(x+2)}=\frac{3}{x+2}$
$(\frac{x}{x+2}y)'=\frac{3x}{(x+2)^2}$
$\frac{x}{x+2}y=3\int \frac{x}{(x+2)^2}dx$
$\frac{x}{x+2}y= 3\int \frac{1}{x+2}dx - 6\int\frac{1}{(x+2)^2}dx$
$\frac{x}{x+2}y= 3 ln|x+2| + \frac{6}{x+2}+c$
I tested this solution for when c=0, but it failed. Can anyone spot my mistake?