diferential equations

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Question 1

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

		q = 8 lnx
		q = e8/x
		q =
		q = ln

5 points

Question 2

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

		y = 12 + Ce-3x
		y = 4 + Ce-3x
		y = + Ce3x
		y = 4 + Ce-12x

5 points

Question 3

Find the particular solution determined by the given condition. y' = ; y = 21 when x = 1

		y = 5 ln x + 2.5
		y = ln x + 19
		y = 5 ln x + 21
		y = ln x + 21

5 points

Question 4

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.

		1400
		350
		4.9
		700

5 points

Question 5

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

		y = + e2x + Ce-2x
		y = + Ce-2x
		y = + Ce2x
		y = 21 + Ce2x

5 points

Question 6

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

Question 7

Find the particular solution determined by the given condition. f'(x) = 3x2 - 2x; f(0) = 18

		f(x) = x3 + 2x2 + 18
		f(x) = 3x3 + x2 + 18
		f(x) = x3 - x2 + 18
		f(x) = 3x3 + 2x2 + 18

5 points

Question 8

Solve. =

		y = ±
		y = x + C
		y = x + C
		y = ±

5 points

Question 9

Solve. = 8x7y

		y = 8Cx8ex8
		y = 8Cx7ex7
		y = Cex8
		y = 8Cx8ex7

5 points

Question 10

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 - 10ekt
		V = 29 - 10e-kt
		V = 39 - 39e-kt
		V = 39 - 10e-kt

5 points

Question 11

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

		24x3 - 20x2 + C
		24x3 - 10x2 + C
		72x3 - 20x2 + C
		72x3 - 10x2 + C

5 points

Question 12

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.

		300
		150
		600
		2.4

5 points

Question 13

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

		6x3 + C
		18x3 + C
		x3 + C
		+ C

5 points

Question 14

Solve. 3y2 = 7x

		y =
		y = -
		y = -
		y =

5 points

Question 15

		y = 100t + 5000 + 5000e0.02t
		y = -100t + 5000 + 5000e-0.02t
		y = -100t - 5000 + 5000e0.02t
		y = 100t + 5000 + 5000e-0.02t

5 points

Question 16

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 = - + Cex2/2
		y = - + Ce-x2

5 points

Question 17

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 = + 2x + Ce-x2
		y = 21 + Cex2
		y = + Cex2

5 points

Question 18

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

		- 16x + C
		x3 - 16x + C
		2x2 - 16 + C
		- x + C

5 points

Question 19

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

		6e3x + C
		e3x + C
		2e3x + C
		e3x + C

5 points

Question 20

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

		y = 4x2 + 10x - 21
		y = 2x2 + 10x - 21
		y = 2x2 + 10x - 10.5
		y = 4x2 + 10x - 10.5

5 points

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