Question

1. By hand, sketch the slope field for the DE x ′ = x(1 − x/4) in the window 0 ≤ t ≤ 8, 0 ≤ x ≤ 8 at the integer lattice points. What is the value of the slope field along the lines x = 0 and x = 4? Show that x(t) = 0 and x(t) = 4 are constant solutions to the DE.

2. Draw several isoclines of the differential equation x ′ = x 2 + t 2 , and from your plots determine, approximately, the graphs of the solution curves.

3. Draw the nullclines for the equation x ′ = 1 − x 2 . Graph the isoclines, or the locus of points in the plane where the slope field is equal to −3 and +3.

Answer #1

**2)**

**Given that**

**the differential equation ==>x ′ = x 2 + t
2**

**A few isoclines
are given below:**

**From this, the
graphs of the solution curves are
approximately:**

**Since
for some constant
**

**3)**

**Nullclines of
which are given below**

**Isoclines where the slope field is equal to -3 and +3 is
given below:**

**
which is impossible and
**

**The region where the slope field is between -3 and +3 is
given below:**

In the right-half tx plane (t ≥ 0), plot the nullclines of the
differential equation x′ = 2x2(x − 4√t). Determine the sign of the
slope field in the regions separated by the nullclines. Sketch the
approximate solution curve passing through the point (1,4). Why
can’t your curve cross the x = 0 axis?

Consider the differential equation dy/dx= 2y(x+1)
a) sketch a slope field
b) Show that any point with initial condition x = –1 in the 2nd
quadrant creates a
relative minimum for its particular solution.
c)Find the particular solution y=f(x)) to the given differential
equation with
initial condition f(0) = 2
d)For the solution in part c), find lim x aproaches 0
f(x)-2/tan(x^2+2x)

1. Sketch the direction field for the following differential
equation dy dx = y − x. You may use maple and attach your graph.
Also sketch the solution curves with initial conditions y(0) = −1
and y(0) = 1.

sketch the slope field and some representative solution curves
for the given differential equation y′ =x+y
Please explain I would like to understand the concept please not
just the answer.
per the solution book, I dont understand why the solution after
the table uts y=-x+1 and after fiferentiate how is the answer 1+x+y
and why do we integrate at the end
thank you!

Sketch the slope field for y′ = y − t 2 as well as solutions
that satisfy initial conditions (a) y(0) = −1, (b) y(0) = 0, (c)
y(0) = 1.

Use
a slope field plotter to plot the slope field for the differential
equation
dy/dx=sqrt(x-y)
and plot the solution curve for the initial condition
y(2)=2

Consider the direction field of the differential equation
dy/dx = x(y − 8)2 − 4,
but do not use technology to obtain it. Describe the slopes of
the lineal elements on the lines
x = 0,
y = 7,
y = 8,
and
y = 9.
x
=
0
y
=
7
y
=
8
y
=
9

Sketch the flow field defined by u = 3y and v = 2 for the field
range given by 0 ≤ x ≤ 4 and 0 ≤ y ≤ 4. Find the magnitude and
acceleration at the point (3, 4). [Use M, L, T system of units].
[To calculate the velocities at all 25 points of the grid you may
set up on MS Excel Worksheet and submit the MS Excel file or its
screen shot]

Consider the equation:
x'=x^3-3x^2+2x
sketch the phase line. solve the equation and sketch the graphs
of some solutions including at least one solution with values in
each interval above, below and between the critical points.
identify critical points as stable or unstable

Assignment #3 Modeling and the Geometry of Systems 1. For this
problem, we study the nonlinear differential equation: dx dt = y dy
dt = x − x^3 − y^3 a) Algebraically determine all of the equilibria
to the differential equation . b) For a solution {x(t), y(t)} with
{x(0), y(0)} = {x0, y0}, use your phase diagram to describe the
long term behavior of the solution. 1. {x0, y0} = {1, 1} 2. {x0,
y0} = {−1, −1} 3....

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