Asystem - f(x, y). -gix. y) is given. solve the equation dy gixy) to find the to find the trajectories of the given system. use a computer system or graphing calculator to construct a phase portrait and direction field for the system, and thereby identify visually the apparent character and stability of the critical point(0, 0) of the given system. = - 4y (4+5x2 + 4y? ) y = x(4+ 5x2 + 4y? ) the general solution of the system is =c, for c> 0. (type an expression using x and y as the variables.) enter your answer in the answer box and then click check answer. parts 2 clear all check answers remaining

Y =-(x⁻5)(x+6) =-(x²- 5x+6x-30)=-x²+x+30

y int =+30, (0,30)

zeros : (-x+5)=0 (x+6)=0, x=5, x=-6 can be written as (5,0), (-6,0)

y=-x²+x+30

y-30 = -x²+x

y-30-(1/2)² = -x²-2*1/2*x +(1/2)²

y-301/4 = -(x -1/2)²

y-(30 1/4) = -(x -1/2)²

vertex(1/2, 30 1/4)

axis x=1/2

should be something like this