This important problem was first studied by Briot and his friend Bouquet and, before Bendixson worked on it, had recently been investigated by Poincaré . Poincaré had obtained a qualitative description of the integral curves but it was Bendixson who gave a quantitative description near the singular points.
Ang mahalagang mga problema ay unang-aral sa pamamagitan ng Briot at ang kanyang mga kaibigan at palumpon, bago Bendixson nagtrabaho sa mga ito, ay kamakailan-lamang na nai-investigated by Poincaré. Poincaré had nakuha ng husay ng isang paglalarawan ng mahalaga kurva ngunit ito ay Bendixson na ibinigay ng dami ng isang paglalarawan ng malapit sa isahan na puntos.