6 Consider the following six direction fields and nine systems of differential equa- tions: (a) (c) (b) (d) (i) (iv) (vii) d.x = (x+1)(y2 -1) dt dt =-x' +2x - 1 =T- dt dy dy dy 12 - 1 = x2 - 2x + 1 It 12 - 1 dt It (ii) (v) (viii) dx dt = (x -1)(y - 1) dt = (1- x)(y+1) dt - = -y' + 2y - 1 dy - = (x+ 1)(y+ 1) dy dy = (x+1)(y -1) It It = y2 + 2y + 1 dt (iii) (vi) (ix) d.x dx = (x2 -1)(y - 1) -x' + 2x - 1 - -x2 - 2x - 1 dt dt dt dy dy dx =-y- 1 It = -x2 - 2x - 1 dt -y? + 1 dt