Thanks for the reply,
my bcs are y(-1)=0, y(1)=0, y'(-1)=beta1, y'(1)=(beta1^2+4A)^(1/2) and y must also satisfy (integral y dx, x=-1..1)=2/3.
I have a third order ode, 2 unknowns and 5 conditions so I have enough for a solution.
This does mean y''' is singular at x=-1, 1 but that is...