Question

Consider the dynamical system below.

dx/dt = -x+2y-4

dy/dt = -x-2y

a.Sketch the nullclines for this system

b. Find the equilibrium point

c. From the initial point (0,2), and using a **Δ**t
value of 0.2, compute the current position after one iteration.

Answer #1

Solve the following system of differential equations:
dx/dt =x+2y
dy/dt =−x+3y

Consider the system [ x' = -2y & y' = 2x] . Use dy/dx to
find the curves y = y(x).
Draw solution curves in the xy phase plane. What type of
equilibrium point is the origin?

Initial value problem : Differential equations:
dx/dt = x + 2y
dy/dt = 2x + y
Initial conditions:
x(0) = 0
y(0) = 2
a) Find the solution to this initial value problem
(yes, I know, the text says that the solutions are
x(t)= e^3t - e^-t and y(x) = e^3t + e^-t
and but I want you to derive these solutions yourself using one
of the methods we studied in chapter 4) Work this part out on paper
to...

consider the following systems of rate of change equations
system A : dx/dt=3x(1-x/10)-1/20xy , dy/dt=-5y+xy/20, system B:
dx/dt=3x-xy/100, dy/dt=15y(1-y/17)+25xy. in both of these systems,x
and y refer to the number of two different species at time t.In
particular, in one of these systems, the prey is large animals and
the predators are small animals, such as piranhas and humans. Thus
it takes many predators to eat one prey, but each prey eaten is a
tremendous benefit for the predator population....

(dx/dt) = x+4z
(dy/dt) = 2y
(dz/dt) = 3x+y-3z

Use the Laplace transform to solve the given system of
differential equations. dx/dt=x-2y dy/dt=5x-y x(0) = -1, y(0) =
6

Consider the following linear system (with real eigenvalue)
dx/dt=-2x+7y
dy/dt=x+4y
find the specific solution coresponding to the initial values
(x(0),y(0))=(-5,3)

dx/dt - 3(dy/dt) = -x+2
dx/dt + dy/dt = y+t
Solve the system by obtaining a high order linear differential
equation for the unknown function of x (t).

Find the general solution to the system:
dx/dt = -4x + 3y
dy/dt = -5x/2 + 2y

dx
dt
= y − 1
dy
dt
= −3x + 2y
x(0) = 0, y(0) = 0

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