> > If I have correctly evaluated > > dy/dx to be = [4(x^3) + 2Ax + 4x(y^2) - By]
No. You must differentiate your equation w.r.t. x, treating y as a function of x applying the chain-rule correctly. You then end up with equation (*) and - if you want - equation (**) comes next. But you don't need it. Just set y' = 0 in (*) since you are only interested in extrema. Then you get the equation:
4(x^3) + 2Ax + 4x(y^2) - By = 0 as a necessary condition for y' = 0.
> > and if it is proper to set this then equal to zero > to give a new equation that could be merged with the original to get rid > of the cumbersome XY terms - then that i failed to do.
Multiply your new equation by x and add it to the original one, that gets rid of the xy-term. I get:
(***) 5x^4 + y^4 + 3Ax^2 - Ay^2 + 6x^2y^2 + C = 0
> > I've tried completing squares etc but can not get rid of composite XY terms. > > If I could eliminate X and get a generalised Y-Only equation > then I could manage the rest.
Can you handle (***)? This is a quadratic equation in X=x^2 and Y=y^2.
> > Any help would be appreciated > > Mervyn Mc Crabbe >