Suppose the non-linear system dx / dt = f(x, y). dyldt = g(x,y) has a fixed point at (x*, y*). Derive the linearisation of the system about (x*, y*). Under what circumstances are the solution paths of the non-linear system close to those of the linearisation? In a model of pollution, capital X and pollution P satisfy the pair of differential equations dK / dt = K(sK ] -5), dP/ dt = K - P where 00, y > 0 and B>1. Find the fixed point (K*, P*) satisfying K* > ( and P* > 0 and show it is locally stable for the non-linear system. Find an explicit expression for K(t) when K(0) =K, 2 0, and find its limit as => 00