Given the initial shape of the longitudinal axis of a curved bar is given by
y0(x) = a*sin(Pi*x/L)

where a is a constant and L is the length of the bar

and proceeding to calculate the deflections due to deformation from the diff. eq.

EI (dy1/dx) = -P(y0+y1)

the ode for deflections is obtained

dy1/dx + k*y1 = -k*a* sin(Pi*x/L)

where k is a constant = sqrt (P/EI)

I am able to solve the ode for 2 sets of boundary conditions:

1) zero displacement at the ends: y1(0) = 0 , y1(L) = 0

 2) zero rotation at the ends: D(y1(0)) = 0, D(y1(L) ) = 0

However, I cannot apply the boundary conditions of zero displacement and rotation simultaneously at both ends, i.e., 4 boundary conditions, which is greater than the order of the ode.  Are there other solution techniques that I can employ to allow the specification of a number of boundary conditions that exceed the order of the ode?

Thank you for your assistance.


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