 As the latter can be classified according to the properties of the fundamental curve that remains unchanged under a rational transformation, Clebsch proposed to classify the transcendent functions defined by differential equations according to the invariant properties of the corresponding surfaces "f" = 0 under rational one-to-one transformations.From 1870, Sophus Lie's work put the theory of differential equations on a better foundation.He showed that the integration theories of the older mathematicians can, using Lie groups, be referred to a common source, and that ordinary differential equations that admit the same infinitesimal transformations present comparable integration difficulties.