Question

Consider the following system of differential equations dx/dt = (x^2 + 2x + 1)(x^2 − 4x + 4) dy/dt = xy − 1

Which of the following is not an equilibrium point of the above system? (A) (3, 1/3 ) (B) (−1, −1) (C) (1, 1) (D) (1, 3)

Answer #1

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

Use the Laplace transform to solve the given system of
differential equations. dx dt = −x + y dy dt = 2x x(0) = 0, y(0) =
2

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

Solve the following system of ordinary differential
equations.
2 dx/dt − 2 dy /dt − 3x = e (n+1)t
2 dx/dt + 2 dy/dt + 3x + 8y = 2

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....

Homogenous Differential Equations:
dy/dx = y - 4x / x-y
dy/dx = - (4x +3y / 2x+y)

Solve the given system of differential equations by systematic
elimination. 2 dx/dt − 6x + dy/dt = e^t
dx/dt − x + dy/dt = 6e^t

Solve the system of differential equations using laplace
transformation
dy/dt-x=0,dx/dt+y=1,x(0)=-1,y(0)=1

1. Solve the following differential equations.
(a) dy/dt +(1/t)y = cos(t) +(sin(t)/t) , y(2pie) = 1
(b)dy/dx = (2x + xy) / (y^2 + 1)
(c) dy/dx=(2xy^2 +1) / (2x^3y)
(d) dy/dx = y-x-1+(xiy+2) ^(-1)
2. A hollow sphere has a diameter of 8 ft. and is filled half way
with water. A circular hole (with a radius of 0.5 in.) is opened at
the bottom of the sphere. How long will it take for the sphere to
become empty?...

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

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