Verifying Buckling Solution with NDSolve/DSolve

[Aladdin123]

Hi I am trying to verify my manual solution for this problem by any way, so I tried NDSolve, and DSolve, in mathematica with no success. I don't need it in mathematica I just need any way poosible, even matlab, or any other numeric way/soltuion. Can some one help, or even give me the final numbers :D I need the first 3 alphas for a buckling.

 

[jedishrfu]

I hope you realize that your request is a bit too much to ask.