Let st it and nt be the savings investment and national

Question

Let S(t), I(t) and N(t) be the Savings, Investment and National Income at time t. Domar Macro model assumes that savings are proportional to the national income, and that all savings are invested proportional to the rate of increase of national income. i. Formulate a mathematical model using differential equations with the given assumptions. ii. Solve the differential equations and comment on the dynamics of the model, assuming y(0)=y_0 (y sub 0).