# Asystem – f(x, y). -gix. y) is given. solve the equation dy gixy) to find the to find the trajectories of the given system.

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

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1. galaalexa says:

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