6) A student buys a classical estate at K30. However the value of the estate is known to change. According to the following differential equation. dy 4 - dt -+ y = 12 a) Find the time path of the value of the estate b) If he auctions the estate at exactly t = 5 , what should be the reservation price? 7) Tet for the exactness of following the differential equation and find general solution by an appropriate technique. 4yt 3 dy dt -+ 6y62 +2 = 0 8) By method of iteration, solve the following difference equation. a) yt-1 = 0.5yt-1 + 4 b) yt = 0.6yt-1 C) yt+1 = Vt+li yo = 10 d) yt+1 = 0.3yt ; yo = 9 9) For each of the following difference equations, find yc, yp and the definite solution. a) yt+1 + 3yt = 4; yo = 4 b) 2yt+1 - Vt = 6; yo = 6 10) the nature of the following time paths: a) yt = 2(3) + 5 b) yt = -3(-0.25)* + 2