I have a sequence of differential equations, which can be solved recursively, i.e, the solution of the first equation is necessary to solve the second equation.

Consider for example

$\frac{\partial}{\partial s}(\frac{1}{\epsilon^2}I_{-2}+\frac{1}{\epsilon} I_{-1} +I_0)=\frac{1}{\epsilon^2}f_0I_{-2}+\frac{1}{\epsilon}(f_0I_{-1}+f_1I_{-2})+(I_{-1}f_0+I_0f_1)$

Where $f_0\; \text{and}\; f_1$ are provided. The differential equations we will get from here are

$\frac{\partial}{\partial s}I_{-2}=f_0I_{-2}$

$\frac{\partial}{\partial s}I_{-1}=f_0I_{-1}+f_1I_{-2}$

and so on.

Is there any hope for solving these type of problem in mathematica? I could not try anything so far.