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

[tim85ruhruniv]

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 can't seem to find it... any suggestions ??

\[<br /> (c_{o}+xk)y&#039;&#039;+ky&#039;=0\]

with ths usual boundary conditions
\[y\left(0\right)=y_{0}\qquad y\left(l\right)=y_{l}\]<br />

c and k are constants and they are related
here is the relation if it is of any additional help...
\[<br /> \frac{c_{l}-c_{o}}{l}=k\]

thanks a lot :)

 

[tim85ruhruniv]

phew after some hits and misses got it finally :)

\[<br /> y=ln\left(c_{o}+xk\right)\]

seems to solve the equation...