xy^2 + y^3 = y(x^2 + 1)

The given equation is $$xy^2 + y^3 = y(x^2 + 1)$$.

Expand the right side: $$y(x^2 + 1) = yx^2 + y$$.

The equation becomes $$xy^2 + y^3 = yx^2 + y$$.

Rearrange the terms: $$y^3 + xy^2 - yx^2 - y = 0$$.

Factor out $$y$$: $$y(y^2 + xy - x^2 - 1) = 0$$.

This implies either $$y = 0$$ or $$y^2 + xy - x^2 - 1 = 0$$.