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Solve ODE numerically

I'd like to solve this ODE: (y')^2=(1-y^2)*(y^2)/(y^2+a) where a is a nonnegative constant. After that, I'd like to get two solutions: y(x0)=p and y(x1)=q, and obtain the difference x0-x1 numerically (It seems that y may be periodic, and the smallest difference is preferred). I got stuck after using desolve to obtain the function. What should I do?