Plz answer this as soon as possible

Task 6 (6.1) The following differential equations system is given: Start2 .1=4 (1) a) For which values of a do you expect vibrations in r(t)? Explain. b) For which values of a do you expect konvergence? Explain. (6.2) In an economy with a constant population output is produced with falling marginal product Y = K*. The investments are equal to the savings and a constant saving rate s is assumed. The capital stock is written off at the rate o. Then the equation for the development of the capital stock is K = s K* -oK (2) Production causes emissions that accumulate in the air. The pollution decays with the rate 7. This results in the following differential equation for pollution P: P = K -nP with b>1 (3) a) Find equilibria for the differential equations system b) Draw a K-P-phase diagram and explain your solution. c) How does the position of the isoclins change if the depreciation rate o increases and if the emission elesticity b is reduced? Explain your solution. (6.3) A company produces the quantity u(t) and has an inventory stock of x(t). A fixed portion a of the production is transferred to the warehouse and the rest is sold at a price p. So the inventory increases by a - u(t). The company wants to maximize its profit. The production costs are given by u(t)', the cost for the warehouse is c-r(t). The initial inventory stock is r(0) = To and the initial production is u(0) = up are also given. This results in the following optimization