% CURVES plots two implicitly-defined curves, for which 
%        we find their intersection by Newton's:
%
%            x^3 + xy - y^3 = 5
%           e^(xy) - sin(y) = arctan(x)

r = -3:.01:3;
[xx,yy] = meshgrid(r,r);
contour(xx,yy,xx.^3+xx.*yy-yy.^3-5,[0 0],'r')
hold on
contour(xx,yy,exp(xx.*yy)-sin(yy)-atan(xx),[0 0])
hold off
grid on

% note:     x^3 + xy - y^3 = 5
%          e^(xy) - sin(y) = - arctan(x)
% don't intersect
