2nd Order ODE,Homogeneous,Non-Constant Coeff.

Hi,

I am trying to guess the solution for this i am sure the solution involves a ln(x) so that i can reduce the order to find the general solution but i just cant seem to find it... any suggestions ??

$$$(c_{o}+xk)y''+ky'=0$$$

with ths usual boundary conditions
$$$y\left(0\right)=y_{0}\qquad y\left(l\right)=y_{l}$$$

c and k are constants and they are related
here is the relation if it is of any additional help...
$$$\frac{c_{l}-c_{o}}{l}=k$$$

thanks a lot :)

$$$y=ln\left(c_{o}+xk\right)$$$