Utilization of Ramanujan-type Eisenstein series in the generation of differential equations

In his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical η-functions and h-functions with the help of the Ramanujan-type Eisenstein series. Moreover, we present particular identities that incorporate Eisenstein series of different levels and h-functions, thereby establishing links between class one infinite series and h-functions.