Calculus homework

Q U E S T I O N 1 1. Find the particular solution determined by the given condition.

f'(x) = 3x2 - 2x; f(0) = 18

f(x) = 3x 3 + 2x2 + 18

f(x) = 3x 3 + x2 + 18

f(x) = x 3 - x2 + 18

f(x) = x 3 + 2x2 + 18

5 points Q U E S T I O N 2

1. Find the general solution for the differential equation. y ' = 2e3x

2e 3x + C

6e 3x + C

e3x + C

e3x + C

5 points Q U E S T I O N 3

1. Solve the problem. If a population is changed by either immigration or emigration, a model for the population is

where y is the population at time t and f(t) is some function of t that describes the net effect of the emigration/immigration. Assume that k = 0.02 and y(0) = 10,000. Solve this differential equation for y, given that

y = 100t + 5000 + 5000e -0.02t

y = 100t + 5000 + 5000e0.02t

y = -100t + 5000 + 5000e -0.02t

y = -100t - 5000 + 5000e0.02t

5 points Q U E S T I O N 4

1. Solve the problem. The logistic differential equation

= 0.08P(300 - P) describes the growth of a population P, where t is measured in years. Find the limiting population.

600

150

2.4

300

5 points Q U E S T I O N 5

1. Solve the problem. If a population is changed by either immigration or emigration, a model for the population is

where y is the population at time t and f(t) is some function of t that describes the net effect of the emigration/immigration. Assume that k = 0.02 and y(0) = 10,000. Solve this differential equation for y, given that

y = 1100t - 55,000 + 65,000e -0.02t

y = -1100t - 55,000 + 65,000e0.02t

y = 1100t + 55,000 + 65,000e -0.02t

y = -1100t - 55,000 + 65,000e -0.02t

5 points Q U E S T I O N 6

1. Solve.

= 8x7y

y = Cex8

y = 8Cx7ex7

y = 8Cx8ex7

y = 8Cx8ex8

5 points Q U E S T I O N 7

1. Solve.

=

y = ±

y = x + C

y = x + C

y = ±

5 points Q U E S T I O N 8

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. 5y' - 10xy - x = 0

y = + Ce-x2/2

y = - + Cex2

y = - + Ce-x2

y = - + Cex2/2

5 points Q U E S T I O N 9

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. y' + 2y = 21

y = + Ce2x

y = 21 + Ce 2x

y = + e2x + Ce-2x

y = + Ce-2x

5 points Q U E S T I O N 1 0

1. Solve the problem. The logistic differential equation

= 0.07P(700 - P) describes the growth of a population P, where t is measured in years. Find the limiting population.

700

4.9

350

1400

5 points Q U E S T I O N 1 1

1. Find the particular solution determined by the given condition. y' = 4x + 10; y = -21 when x = 0

y = 2x 2 + 10x - 10.5

y = 4x 2 + 10x - 10.5

y = 2x 2 + 10x - 21

y = 4x 2 + 10x - 21

5 points Q U E S T I O N 1 2

1. Find the general solution for the differential equation. y ' = 18x2

x 3 + C

+ C

6x 3 + C

18x 3 + C

5 points Q U E S T I O N 1 3

1. Solve the problem.

The growth rate of a certain stock is modeled by where V = the value of the stock, per share, after time t (in months), and k = a constant. Find the solution to the differential equation in terms of t and k.

V = 39 - 39e -kt

V = 29 - 10e -kt

V = 39 - 10ekt

V = 39 - 10e -kt

5 points Q U E S T I O N 1 4

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. y' + 3y = 12

y = 4 + Ce -12x

y = 4 + Ce -3x

y = + Ce3x

y = 12 + Ce -3x

5 points Q U E S T I O N 1 5

1. Find the general solution of the differential equation, or the particular solution if an initial condition is given. y' + 2xy = 21x

y = + Ce-x2

y = 21 + Cex2

y = + 2x + Ce-x2

y = + Cex2

5 points Q U E S T I O N 1 6

1. Find the general solution for the differential equation. y ' = x - 16

2x 2 - 16 + C

- x + C

x 3 - 16x + C

- 16x + C

5 points Q U E S T I O N 1 7

1. Solve the problem.

Find the demand function q = D(x), given that E(x) = and q = e when x = 8.

q = e8/x

q = 8 lnx

q = ln

q =

5 points Q U E S T I O N 1 8

1. Find the general solution for the differential equation. y ' = 72x2 - 20x

72x 3 - 10x2 + C

72x 3 - 20x2 + C

24x 3 - 20x2 + C

24x 3 - 10x2 + C

5 points Q U E S T I O N 1 9

1. Find the particular solution determined by the given condition.

y' = ; y = 21 when x = 1

y = 5 ln x + 21

y = ln x + 21

y = ln x + 19

y = 5 ln x + 2.5

5 points Q U E S T I O N 2 0

1. Solve.

3y2 = 7x

y = -

y =

y = -

y =

5 points