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
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