2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116425A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $Γ_0(2)$ of the modular group $SL_2(\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known Ramanujan equations, as well as the Chazy and Darboux-Halphen equations associated with the modular group. The general solutions of these equations can be realized in terms of the Schwarz trianle function $S(0,0,1/2; z)$.PACS numbers: 02.30.Ik, 02.30.Hq, 02.10.De, 02.30.GpNumber TheoryClassical Analysis and ODEs11F03; 11F11text