Question

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)

Answer #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

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.

(1 point)
In this problem we consider an equation in differential form
Mdx+Ndy=0Mdx+Ndy=0.The equation
(4e−2y−(20x4y5e−x+2e−xsin(x)))dx+(−(20x5y4e−x+8e−2y))dy=0(4e−2y−(20x4y5e−x+2e−xsin(x)))dx+(−(20x5y4e−x+8e−2y))dy=0
in differential form M˜dx+N˜dy=0M~dx+N~dy=0 is not exact.
Indeed, we have
M˜y−N˜x=

Solve the Homogeneous differential equation
(7 y^2 + 1 xy)dx - 1 x^2 dy = 0
(a) A one-parameter family of solution of the equation is y(x)
=
(b) The particular solution of the equation subject to the
initial condition y(1) =1/7.

solve the differential equation
(2y^2+2y+4x^2)dx+(2xy+x)dy=0

consider the equation y*dx+(x^2y-x)dy=0. show that the equation
is not exact. find an integrating factor o the equation in the form
u=u(x). find the general solution of the equation.

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...

Solve the Differential Equation:
(2y^4 + xy)dx - (6x^2) dy= 0

Find the particular integral of the differential equation
d2y/dx2 + 3dy/dx + 2y = e −2x
(x + 1). show that the answer is yp(x) = −e −2x ( 1/2
x2 + 2x + 2)

Consider the initial value problem
dy dx
=
1−2x 2y
, y(0) = − √2
(a) (6 points) Find the explicit solution to the initial value
problem.
(b) (3 points) Determine the interval in which the solution is
deﬁned.

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