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

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The discussion centers on solving a second-order ordinary differential equation (ODE) of the form \((c_{o}+xk)y''+ky'=0\) with boundary conditions \(y(0)=y_{0}\) and \(y(l)=y_{l}\). The solution involves the natural logarithm function, specifically \(y=\ln(c_{o}+xk)\), which effectively reduces the order of the equation. Constants \(c\) and \(k\) are related by the equation \(\frac{c_{l}-c_{o}}{l}=k\). The user successfully derived the general solution after some initial challenges.

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tim85ruhruniv
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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 ??

[tex]\[<br /> (c_{o}+xk)y''+ky'=0\][/tex]

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

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

thanks a lot :)
 
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phew after some hits and misses got it finally :)

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

seems to solve the equation...
 

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