How can this equation be solved?
By separation of variables.
Now you can integrate both sides.
The integral of the dx side requires decomposition into partial fractions.
I'm a bit rusty in solving ODE's and was having a hard time trying to solve this one..
dx/(ax(b-x)) = dx/abx + dx/ab(b-x)
= dx/abx - d(b-x)/ab(b-x)
and then you can integrate these terms.
Separate names with a comma.