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Particular Solution of 4th degree differential equation (column buckling)

I'm trying to use Mathematica to solve the Euler Column buckling problem (http://www.continuummechanics.org/cm/columnbuckling.html), but its not working out. Mathematica only shows me the zero solution. Is there any way of getting the no zero displacements solutions? For now, what I have is basically this:

equation = EIy''[x] + Py[x] == 0

DSolve[{equation, y[0] == 0, y[L] == 0}, y[x], x]

Out[143]= {{y[x] -> 0}}

Thanks, Luís Valarinho
POSTED BY: Luis Valarinho
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Hello Kay!

Thanks for the suggestion. What I did actually was using the nomenclature that we use in Civil Engineering But you're right, it can lead to mistakes. Thanks for the other suggestions too. I was actually wondering if it is possible to do it in one step. We cannot ask Mathematica to give all the possible solutions? Or adding an assumption that C[2] should be different than zero? (something that is not necessarily truth).

Thanks, Luís Valarinho
POSTED BY: Luis Valarinho
POSTED BY: Kay Herbert

Ok, thanks!
POSTED BY: Luis Valarinho

The solution given is correct but it isn't the only solution. Yes, you'll have to handle the boundary condition at L separately.
POSTED BY: Frank Kampas

So, if I understood Mathematica doesn't solve the equation automatically.

The last boundary condition will have to be me adding it, right?
POSTED BY: Luis Valarinho

Replace y[L] ==0 with y'[0] == yp0 and then combine y[L] ==0 with the solution you get.
POSTED BY: Frank Kampas
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