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 + Ce3x y = 4 + Ce-3x y= + Ce3x y = 4 + Ce12x 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 + 65,000e0.02t 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 + 1 8 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 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 + 5000e0.02t y = -100t + 5000 + 5000e0.02t 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 Save and Submit Click Save and Submit to save and submit. Click Save All Answers to save all answers. QUESTION 1 Solve the problem. Find the demand function q = D(x), given that E(x) = and q = e when x = 8. q = 8 ln x 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 + Ce3x y= + Ce3 x y = 4 + Ce12x 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. 140 0 350 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 + Ce2x y = 21 + Ce2x y= 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 + 65,00 0e-0.02t y = -1100t - 55,000 + 65,00 0e0.02t y = 1100t + 55,000 + 65,00 0e-0.02t y = -1100t - 55,000 + 65,00 0e-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 = 8Cx8e x8 y = 8Cx7e x7 y = Cex8 y = 8Cx8e x7 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 - 10 ekt V = 29 - 10 e-kt V = 39 - 39 e-kt V = 39 - 10 e-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. 30 0 15 0 60 0 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 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 + 5000 e0.02t y = -100t + 5000 + 5000 e-0.02t y = -100t - 5000 + 5000 e0.02t y = 100t + 5000 + 5000 e-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=- + Cex 2 y=2/2 + Cex 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 - 2 1 y = 2x2 + 10x - 2 1 y = 2x2 + 10x - 1 0.5 y = 4x2 + 10x - 1 0.5 5 points S AV E A N D S U B M I T Click Save and Submit to save and submit. 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