Question: help in solving 4th order ODE with boundary conditions that are procedures

hi!

I am trying to solve an ODE for w(x);

E - a parameter
MI - a parameter
w(x) - Transverse deflection
q(x) - Transverse force on the beam with respect to x
G - a parameter
A - a parameter
ap - a parameter
si - a parameter
mysol1 - differential equation to be solved with boundary conditions (bc1,bc2,bc3 and bc4) applied



> with(CodeGeneration);
> with(PDEtools);
> declare(prime = x);
> b := ap/(l+si)^1.5;
> NULL;
> q := proc (x) options operator, arrow; ap/(x+si)^1.5-b end proc;
> bc1 := w(0) = 0;
> bc2 := (E*MI*(diff(w(x), `$`(x, 3)))/(A*G)+(diff(q(x), x))/(A*G)^2+diff(w(x), x))(0) = 0;
> bc3 := (-E*MI*(diff(w(x), `$`(x, 3)))/(A*G)-E*MI*(diff(q(x), x))/(A*G)^2)(1) = 0;
> bc4 := (diff(w(x), `$`(x, 2))+q(x)/(A*G))(1) = 0;
> myode := E*MI*(diff(w(x), `$`(x, 4)))+E*MI*(diff(q(x), `$`(x, 2)))/(G*A) = q(x);
> mysol1 := rhs(dsolve({myode, bc2, bc3, bc1, bc4}, w(x)));

when trying to run it for an output, I get an error saying that it is "vague". It seems that Maple is having difficulty understanding the boundary conditions I have applied since they are sort of "procedures" by themselves!

Any help in solving this differential equation analytically will be greatly appreciated!

Thanks.

kclaw.

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