Question: how to solve a system of linear equations + 1 trancendental equation?

Hi

To find the deflection of a bar under buckling I am trying to solve a set of 10 unknowns and 10 equations, with equations like this one:

eq3 := C1*cos(P^(1/2))+sin(P^(1/2))+5*C3+C4 = C5*cos(P^(1/2))+sin(P^(1/2))+5*C7+C8

(the complete file is included)

When I try to solve the system, Maple is able to evaluate all the C's but not P. That makes sense, because P will be a solution of a transcendental equation (something like tan(x)=x) as opposed to the the C's all being linearly dependant.

I've tried in a number of ways to convert the equations to polynomials,  but since there's a transcendental function involved thats not likely to work. Strangely, Maple was able to solve a more simple but similar case using fsolve + specified interval to find P.

Does anyone have an idea that I could try?

Thanks in advance!

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