Differential equation and the Covid 19 Pandemic

The current report has the purpose to highlight the use of difference equations of linear k order with constant coefficients, to resolve not only financial and/or economic issues, but also social problems. Therefore in the first section of the work, there are confronted some preliminary matters regarding the difference equations(ordinary) of k order with some of the resulting problems, of the initial values and values of Cauchy, exceeded with the help of existence and unity theorems. Additionally it is provided a further approach regarding the problem of finding the solution , belonging to a solution domain , of a differential equation which presents itself stable. All this to arrive at the individuation of the general integral so that every problem of Cauchy, that is related to it, is determined. In the second part, the work suggests to put in the analysis a model, presumed the SIR model, that as previously mentioned will be applied to face and better comprehend which are the conditions that trigger the determination, such as the spread or the vanishing of the pandemic itself, provoked by COVID 19.