  In this paper, we show that it is always possible to deform a differential
equation $\partial_x \Psi(x) = L(x) \Psi(x)$ with $L(x) \in
\mathfrak{sl}_2(\mathbb{C})(x)$ by introducing a small formal parameter $\hbar$
in such a way that it satisfies the Topological Type properties of Berg\`ere,
Borot and Eynard. This is obtained by including the former differential
equation in an isomonodromic system and using some homogeneity conditions to
introduce $\hbar$. The topological recursion is then proved to provide a formal
series expansion of the corresponding tau-function whose coefficients can thus
be expressed in terms of intersections of tautological classes in the
Deligne-Mumford compactification of the moduli space of surfaces. We present a
few examples including any Fuchsian system of $\mathfrak{sl}_2(\mathbb{C})(x)$
as well as some elements of Painlev\'e hierarchies.
