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

  • Thread starter Thread starter tim85ruhruniv
  • Start date Start date
  • Tags Tags
    2nd order
tim85ruhruniv
Messages
14
Reaction score
0
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 :)
 
Physics news on Phys.org
phew after some hits and misses got it finally :)

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

seems to solve the equation...
 
There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t). I have seen other good visual representations of...
Back
Top