The algeqtoseries(pol, x, y, order) command computes an expansion of all the branches at the origin.  The equation  defines a multivalued function y(x).

If pos_slopes is specified, only those branches tending to 0 are computed. Note that this function is not designed to compute expansions to a large order. In this case, the differential equation should be used.  For more information, see algeqtodiffeq.