Verifying Buckling Solution with NDSolve/DSolve

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Aladdin123
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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.
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