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Diff Eq 1.3

 

<== Differential Equations
Number Question Answer
See the work
1. Match the following equations with their direction field.

A. Set y equal to zero and look at how the derivative behaves along the x-axis.
B. Do the same for the y-axis by setting x equal to 0
C. Consider the curve in the plane defined by setting y'=0 -- this should correspond to the points in the picture where the slope is zero.
D. Setting y' equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and can be used to construct the direction field picture by hand.

 1. y'=-(2x+y)/(2y)
 2. y'=-2+x-y 
 3. y'=3sin(x)+1+y

A B C

1.A
2.C
3.B                              

Comming Soon
2. Match the following equations with their direction field. Clicking on each picture will give you an enlarged view.

 1. y'x+2y
 2. y'=y(4-y)
 3. y'=xe^(-2x)-2y
 4. y'=2x-1-y^(2)

 

A B

 


C D
1. C
2. D
3. A
4. B
Comming Soon
3. Match the following equations with their direction field.

A. Set y equal to zero and look at how the derivative behaves along the x-axis.
B. Do the same for the y-axis by setting x equal to 0
C. Consider the curve in the plane defined by setting y'=0 -- this should correspond to the points in the picture where the slope is zero.
D. Setting y' equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and can be used to construct the direction field picture by hand.

 1. y'=2sin(x)+1+y
 2. y'=y+2
 3. y'= -(2x+y)/(2y)
 4. y'=e^(-x)+2y

 

A B

C D
1. D
2. A
3. B
4. C
Comming Soon
4. Consider the direction field of some differential equation dy/dt=F(t,y).
(Click on the thumbnail to open a new window with an enlarged image)

Suppose that y(0) = 1. Then y(2) is closest to which value?

A. 0
B. 3
C. -1
D. -3
E. 1
F. -2
G. 2
E Comming Soon
5. A function y(t) satisfies the differential equation
dy/dt= -y^4 -6y^3 +16y^2


(a) What are the constant solutions of this equation?
Separate your answers by commas.
.

(b) For what values of y is y increasing?
<y< .
(a) -8, 0,2
(b) -8<y<2
Comming Soon
6. The graph of the function ƒ(x) is
(the horizontal axis is x.)
Given the differential equation x'(t)=ƒ(x(t)).
List the constant (or equilibrium) solutions to this differential equation in increasing order and indicate whether or
not these equations are stable, semi-stable, or unstable.



-3.5 Stable
-2.5Semistable
-0.5 Unstable
1.5 Stable
Comming Soon
7. Given the differential equation x'=-(x+2.5)(x+0.5)^3(x-1.5)^2(x-3.5).
List the constant (or equilibrium) solutions to this differential equation in increasing order and indicate whether or
not these equations are stable, semi-stable, or unstable.



-2.5 Stable
-0.5 Unstable
1.5Semi-stable
3.5 Stable
Comming Soon