Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1. If a>0 and b>0, the autonomous differential equation dp/dt=P(a-bP) has a solu

ID: 2985219 • Letter: 1

Question

1. If a>0 and b>0, the autonomous differential equation dp/dt=P(a-bP) has a solution that is

a. increasing everywhere

b. decreasing everywhere

c. increasing if 0<P<a/b

d. decreasing if 0<P<a/b

e. increasing if P>a/b

2. The autonomous differential equation d/xt=x(x-1)(x+1) has a solution

a. increasing everywhere

b. decreasign everywhere

c. increasing if 0<x<1

d. decreasing if -1<x<0

e. increasing if x>1

3. In the autonomous differential equation ex/dt=x(1-x), the critical point

a. x=0 is an attractor

b. x=0 is semistable

c. x=1 is an attractor

d. x=1 is a repeller

e. x=1 is semistable

4. The differential equation (x^2+y^2)y'=xy is

a. linear

b. homogeous

c. separable

d. exact

e. Bernoulli

5. The differential equation y'=xe^y/y is

a. linear

b. homogeous

c. separable

d. exact

e. Bernoulli

6. The differential equation xy'=2y+sinx is

a. linear

b. homogeous

c. separable

d. exact

e. Bernoulli

7. The solution of the differential equation y'=xy is

a. y=ce^x

b. y=ce^x^2

c. y=c+e^x

d. y=ce^x^2/2

e. y=c+e^x^2/2

8. The solution of the differential equation y'-y=x is

a. y=x-1+ce^-x

b. y=x^2/2+e^x

c. y=x^2/2+e^-x

d. y=x-1+ce^x

e. y=-x-1+ce^x

9. An integrating factor for the linear differential equation xy’+y=x is

a. 0

b. 1

c. x

d. 1/x

e. e^x

10. An integrating factor for the linear differential equation y’-y/x=x is

a. x

b. x^2

c. 1/x

d. 1/x^2

e. e^-x

Explanation / Answer

1-c

2-e

3-b

4-b

5-a

6-e

7-e

8-d

9-e

10-d