Force, Work, and Energy

For F= -bv^2, the following:

m r''(t) = b*r'(t)^2

r''(t)/r'(t) = b/m*r'(t)

ln|r'(t)| = b/m*r(t)

r'(t) = e^(b/m*r(t))

1 = r'(t) e^(-b/m*r(t))

t+C1 = (-m/b) e^(-b/m*r(t))

(-b/m)*(t+C1) = e^(-b/m*r(t))

ln|(-b/m)*(t+C1)|= -b/m*r(t)

r(t) = (-m/b)*ln|(-b/m)*(t+C1)|

r'(t) = 1/[(-b/m)*(t+C1)]

r'(t) = m/(-bt+m*C1)

r''(t) = -bm/(-bt+m*C1)^2

However, starting from the bolded step, I could have done things differently to obtain a different answer.

ln|(-b/m)| +ln|(t+C1)|= -b/m*r(t)

r(t) = -m/b*ln|(-b/m)| -m/b*ln|t+C1|

r'(t) = (-m/b) / (t+C1)

r''(t) = (-m/b) / (t+C1)^2

I'm not sure what is going on. They both seem correct, but I'm leaning more toward the bottom one. And like before, I run into trouble dealing with the constant of integration. :/

Oh and I just noticed that the units of all three are entirely off. The only way for the units to work is if C1 and C2 have the units of velocity. Then I'm really lost, because I have to choose a C1 and C2. ;_;