  Context: In the last years, a significant number of works have focused on
finding analytic solutions for the chemical enrichment models of galactic
systems, including the Milky Way. Some of these solutions, however, cannot
account for the enrichment produced by Type Ia SNe due to the presence of the
delay time distributions (DTDs) in the models.
  Aims: We present a new analytic solution for the chemical evolution model of
the Galaxy. This solution can be used with different prescriptions of the DTD,
including the single and double degenerate scenarios, and allows the inclusion
of an arbitrary number of pristine gas infalls.
  Methods: We integrate the chemical evolution model by extending the
instantaneous recycling approximation with the contribution of Type Ia SNe. For
those DTDs that lead to non-analytic integrals, we describe them as a
superposition of Gaussian, exponential and 1/t functions using a restricted
least-squares fitting method.
  Results: We obtain the exact solution for a chemical model with Type Ia SNe
widely used in previous works. This solution can reproduce the expected
chemical evolution of the alpha and iron-peak elements in less computing time
than numerical integration methods. We compare the pattern in the [Si/Fe] vs.
[Fe/H] plane observed by APOGEE DR17 with that predicted by the model. We find
the low alpha sequence can be explained by a delayed gas infall. We exploit the
applicability of our solution by modelling the chemical evolution of a
simulated Milky Way-like galaxy from its star formation history. The
implementation of our solution is released as a python package.
  Conclusions: Our solution constitutes a promising tool for the Galactic
Archaeology and is able to model the observed trends in alpha element
abundances versus [Fe/H] in the solar neighbourhood. We infer the chemical
information of a simulated galaxy modelled without Chemistry.
