Chazy equation explained

In mathematics, the Chazy equation is the differential equation

(d ^{3y})/(dx ^{3}) =2 y (d ^{2y})/(dx ^{2}) - 3 \left( (dy)/(dx) \right) ^{2.} It was introduced by as an example of a third-order differential equation with a movable singularity that is a natural boundary for its solutions.

One solution is given by the Eisenstein series

E _{2(\tau)} =1-24 \sum \sigma ^{n =} _{1 (n)q} 1-24 q -72 q ^{2- … .} Acting on this solution by the group SL₂ gives a 3-parameter family of solutions