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MATH 3321 Quiz 6 9/17/14

1. The differential equation that has y= C1x3 +C2 as its general solution is:

(a) y 2y= 0.

(b) xy 2y = 0.

(c) x2y 2y= 0.

(d) y

2xy

= 0.(e) none of the above.

2. The solution of the initial-value problem xy + 3y=ex

x, y(1) = 2 is:

(a) y= ex

x3

ex

x2+

2

x2.

(b) y= x2ex x3ex + 2x3.

(c) y=ex

x

ex

x2+

2

x.

(d) y= ex

x2

ex

x3

+ 2

x3

.

(e) none of the above.

3. The general solution of yy =xy2 x y2 + 1 is:

(a) y2 =Cex22x + 1

(b) y2 1 =ex22x + C

(c) y2 =ex22x +C

(d) y2 1 =Ce2xx2

(e) none of the above.

4. The general solution of y +xy = xy3 is

(a) y= 1

1 + Cex2

(b) y2 = 1

1 + Cex2

(c) y=

1 +Cex

2

(d) y2 = 1

1 + Cex2

(e) none of the above.

5. The general solution of y =x2ey/x + y2

xy

. is

(a) yey/x + xey/x =C xx ln x

(b) yey/x +xey/x =x x ln x + C.

(c) yey/x +xey/x =Cxx ln x

(d) yey/x +xey/x =Cx+x ln x

(e) none of the above.

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6. The family of orthogonal trajectories of y= Ce2x + 1 is:

(a) y2 2y+ x= C

(b) y2 2y+ e2x =C

(c) y2 + 2y+ Cx = 0

(d) y2 + 2y+ Ce2x = 0

(e) none of the above.

7. A sample of 100 grams of radioactive material was present initially and after 3 hours the samplelost 20% of its mass. An expression for the mass of the material remaining at any time t is:

(a) A(t) = 100

4

5

t/3

(b) A(t) = 100

4

5

t/3

(c) A(t) = 1001

5t/3

(d) A(t) = 100

1

5

t/3

(e) None of the above.

8. A biologist observes that a certain bacterial colony triples every 4 hours and after 12 hoursoccupies 1 square centimeter. Assume that the colony obeys the population growth law. The areathe colony occupied when first observed was:

(a) 1

9 sq. cm.

(b) 181

sq. cm.

(c) 1

36 sq. cm.

(d) 1

27 sq. cm.

(e) None of the above.

9. A thermometer is taken from a room where the temperature is 72o F to the outside where thetemperature is 32o F. After 1/2 minute, the thermometer reads 50o F. How many minutesdoes the thermometer have to be outside for it to read 35o F?

(a) 2.12 min

(b) 1.92min

(c) 1.62 min

(d) 1.43 min

(e) None of the above.

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10. The value(s) of such that y= x is a solution of y 5

xy +

9

x2y = 0 is (are):

(a) = 3

(b) = 3

(c) = 3, 3

(d) = 3,1(e) None of the above.

11. x2y 2x y 10 y= 0 has solutions of the form y = x. The general solution of the equation is:

(a) y= C1x2 +C2x

5

(b) y= C1x9 +C2x

1

(c) y= C1x22 +C2x

5

(d) y= C1x2 +C2x

5

(e) None of the above.

12. x2y 6 y= 0 has solutions of the form y= x. A fundamental set of solutions of the equationis:

(a) {e3x, e2x}

(b) {e6x, ex}

(c) {e2x, e3x}

(d) {e6x, ex}

(e) None of the above.

13. The general solution of y 8y + 20y= 0 is:

(a) y= C1e2x cos 4x + C2e

2x sin 4x

(b) y= C1e4x cos 2x + C2e

4x sin 2x

(c) y= C1e10x + C2e

2x

(d) y= C1e5x +C2e

4x

(e) None of the above.

14. A fundamental set of solutions of y 4y 12y= 0 is:

(a)

e4x, e3x

(b)

e6x, e2x

(c)

e2x, e6x

(d)

e4x, e3x

(e) None of the above.

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20. The second order linear differential equation that has y= 3e4x as a solution is:

(a) y4y + (4)y= 0 for any real number .

(b) y4 y + (4 + )y = 0 for any real number .

(c) y + ( + 4)y + 4 y = 0 for any real number .

(d) y( + 4)y + 4 y = 0 for any real number .

(e) None of the above.

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