On some super-congruences for the coefficients of analytic solutions of certain differential equations

In this paper, we prove some congruences involving the coefficients \(\{A_{n}\}_{n=0,1,2,\ldots }\) of the analytic solution \(y_0(z)=\sum _{n=0}^\infty A_nz^n\) of certian differential eqution \({\mathcal {D}}y=0\) normalized by the condition \(y_0(0)=A_0=1\), where \({\mathcal {D}}\) is a 4th-order linear differential operator.