Question: dsolve to get eigenvalues

When I execute the code below, dsolve returns the trivial solution. If I were to apply the BCs by hand I'd conclude that there is a set of eigenvalues associated with the ODE. Is there a way to have Maple produce the eigenvalue equation automatically, or would you typically apply the BCs by hand to find it?

Y_BCs:=y(0)=0, (D@@2)(y)(0)=0, y(L)=0, (D@@2)(y)(L)=0;



Is there another way to specify the derivative BC?


Thank you

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