[enoch]

I'd like to solve the below highly nonlinear ODEs with constraint equations. Eq 1 is a 2nd order ODE, so I need two BCs where only one BC is specified and the other should be determined by Eq2. I have no clue on how to approach this kind of problem and don't know how to use Eq 2. I really appreciate that if you could give me some helps to resolve those constraints in terms of numerics. Thanks.


Governing Equations
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nu: 2*(1+nu+nu^2)*nu'*nu'' + (2*nu+1)*(nu')^3 = 0, (Eq 1)


Boundary Conditions
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nu(-1) = 0.2, nu(1) = alpha (determined by Eq2)

Constraints
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N=integral( nu*dY ) dY from Y=-1 to Y=1, (Eq 2)
Eq 4 should be used to determine alpha