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Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E) ​ Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E) ​


A) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
B) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
C) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
D) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
E) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)

F) A) and B)
G) B) and D)

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At time At time minutes, the temperature of an object is F. The temperature of the object is changing at the rate given by the differential equation . Use Euler's Method to approximate the particular solutions of this differential equation at . Use a step size of . Round your answer to one decimal place. ​ A) 137.1 B) 139.5 C) 147.4 D) 144.6 E) 132.7 minutes, the temperature of an object is At time minutes, the temperature of an object is F. The temperature of the object is changing at the rate given by the differential equation . Use Euler's Method to approximate the particular solutions of this differential equation at . Use a step size of . Round your answer to one decimal place. ​ A) 137.1 B) 139.5 C) 147.4 D) 144.6 E) 132.7 At time minutes, the temperature of an object is F. The temperature of the object is changing at the rate given by the differential equation . Use Euler's Method to approximate the particular solutions of this differential equation at . Use a step size of . Round your answer to one decimal place. ​ A) 137.1 B) 139.5 C) 147.4 D) 144.6 E) 132.7 F. The temperature of the object is changing at the rate given by the differential equation At time minutes, the temperature of an object is F. The temperature of the object is changing at the rate given by the differential equation . Use Euler's Method to approximate the particular solutions of this differential equation at . Use a step size of . Round your answer to one decimal place. ​ A) 137.1 B) 139.5 C) 147.4 D) 144.6 E) 132.7 . Use Euler's Method to approximate the particular solutions of this differential equation at At time minutes, the temperature of an object is F. The temperature of the object is changing at the rate given by the differential equation . Use Euler's Method to approximate the particular solutions of this differential equation at . Use a step size of . Round your answer to one decimal place. ​ A) 137.1 B) 139.5 C) 147.4 D) 144.6 E) 132.7 . Use a step size of At time minutes, the temperature of an object is F. The temperature of the object is changing at the rate given by the differential equation . Use Euler's Method to approximate the particular solutions of this differential equation at . Use a step size of . Round your answer to one decimal place. ​ A) 137.1 B) 139.5 C) 147.4 D) 144.6 E) 132.7 . Round your answer to one decimal place. ​


A) 137.1
B) 139.5
C) 147.4
D) 144.6
E) 132.7

F) A) and E)
G) C) and D)

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E

The logistic function The logistic function models the growth of a population. Identify the value of k. A) 1.7 B) 2.2 C) 0.2 D) 20 E) 0.5 models the growth of a population. Identify the value of k.


A) 1.7
B) 2.2
C) 0.2
D) 20
E) 0.5

F) A) and B)
G) C) and E)

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Solve the differential equation. ​ Solve the differential equation. ​ ​ A) B) C) D) E) ​


A) Solve the differential equation. ​ ​ A) B) C) D) E)
B) Solve the differential equation. ​ ​ A) B) C) D) E)
C) Solve the differential equation. ​ ​ A) B) C) D) E)
D) Solve the differential equation. ​ ​ A) B) C) D) E)
E) Solve the differential equation. ​ ​ A) B) C) D) E)

F) A) and B)
G) B) and D)

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Find the general solution of the differential equation Find the general solution of the differential equation . ​ A) B) C) D) E) . ​


A) Find the general solution of the differential equation . ​ A) B) C) D) E)
B) Find the general solution of the differential equation . ​ A) B) C) D) E)
C) Find the general solution of the differential equation . ​ A) B) C) D) E)
D) Find the general solution of the differential equation . ​ A) B) C) D) E)
E) Find the general solution of the differential equation . ​ A) B) C) D) E)

F) C) and E)
G) A) and E)

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Determine whether the function Determine whether the function is homogeneous and determine its degree if it is. ​ A) homogeneous, the degree is 3 B) homogeneous, the degree is 4 C) not homogeneous D) homogeneous, the degree is 2 E) homogeneous, the degree is 1 is homogeneous and determine its degree if it is. ​


A) homogeneous, the degree is 3
B) homogeneous, the degree is 4
C) not homogeneous
D) homogeneous, the degree is 2
E) homogeneous, the degree is 1

F) A) and B)
G) All of the above

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A conservation organization releases 20 wolves into a preserve. After 2 years, there are 35 wolves in the preserve. The preserve has a carrying capacity of 125. Determine the time it takes for the population to reach 80.


A) 9.020 years
B) 4.875 years
C) 6.259 years
D) 3.692 years
E) 7.884 years

F) B) and C)
G) None of the above

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A 300-gallon tank is full of a solution containing 55 pounds of concentrate. Starting at time A 300-gallon tank is full of a solution containing 55 pounds of concentrate. Starting at time distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred solution is withdrawn at the same rate. Find the quantity of the concentrate in the solution as . ​ A) 30 B) 56 C) 55 D) 0 E) 1 distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred solution is withdrawn at the same rate. Find the quantity of the concentrate in the solution as A 300-gallon tank is full of a solution containing 55 pounds of concentrate. Starting at time distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred solution is withdrawn at the same rate. Find the quantity of the concentrate in the solution as . ​ A) 30 B) 56 C) 55 D) 0 E) 1 . ​


A) 30
B) 56
C) 55
D) 0
E) 1

F) C) and E)
G) A) and B)

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Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E) ​


A) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
B) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
C) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
D) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)
E) Match the logistic differential equation and initial condition with the graph of its solution shown below. ​ ​ A) B) C) D) E)

F) A) and E)
G) None of the above

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The initial investment in a savings account in which interest is compounded continuously is $803. If the time required to double the amount is The initial investment in a savings account in which interest is compounded continuously is $803. If the time required to double the amount is years, what is the annual rate? Round your answer to two decimal places. ​ A) 7.30 % B) 7.70 % C) 13.71 % D) 6.10 % E) 8.70 % ​ years, what is the annual rate? Round your answer to two decimal places. ​


A) 7.30 %
B) 7.70 %
C) 13.71 %
D) 6.10 %
E) 8.70 %
​

F) B) and E)
G) A) and B)

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Find the function Find the function passing through the point with the first derivative . A) B) C) D) E) passing through the point Find the function passing through the point with the first derivative . A) B) C) D) E) with the first derivative Find the function passing through the point with the first derivative . A) B) C) D) E) .


A) Find the function passing through the point with the first derivative . A) B) C) D) E)
B) Find the function passing through the point with the first derivative . A) B) C) D) E)
C) Find the function passing through the point with the first derivative . A) B) C) D) E)
D) Find the function passing through the point with the first derivative . A) B) C) D) E)
E) Find the function passing through the point with the first derivative . A) B) C) D) E)

F) C) and D)
G) B) and E)

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The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours there are 135 bacteria in the culture and after 4 hours there are 390 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. ​ (i) Find the initial population. ​ (ii) Write an exponential growth model for the bacteria population. Let t represent time in hours. ​ (iii) Use the model to determine the number of bacteria after 8 hours. ​ (iv) After how many hours will the bacteria count be 25,000? ​


A) (i) 46.7341; (ii) The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours there are 135 bacteria in the culture and after 4 hours there are 390 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. ​ (i) Find the initial population. ​ (ii) Write an exponential growth model for the bacteria population. Let t represent time in hours. ​ (iii) Use the model to determine the number of bacteria after 8 hours. ​ (iv) After how many hours will the bacteria count be 25,000? ​ A) (i) 46.7341; (ii) ; (iii) 4,566.8441; (iv) 14.1787 hr B) (i) 48.8841; (ii) ; (iii) 5,941.5613; (iv) 16.4067 hr C) (i) 46.7341; (ii) ; (iii) 3,254.11; (iv) 11.8442 hr D) (i) 52.5141; (ii) ; (iii) 8,693.0147; (iv) 18.5179hr E) (i) 54.0741; (ii) ; (iii) 11,345.4782; (iv) 20.2973 hr ; (iii) 4,566.8441; (iv) 14.1787 hr
B) (i) 48.8841; (ii) The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours there are 135 bacteria in the culture and after 4 hours there are 390 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. ​ (i) Find the initial population. ​ (ii) Write an exponential growth model for the bacteria population. Let t represent time in hours. ​ (iii) Use the model to determine the number of bacteria after 8 hours. ​ (iv) After how many hours will the bacteria count be 25,000? ​ A) (i) 46.7341; (ii) ; (iii) 4,566.8441; (iv) 14.1787 hr B) (i) 48.8841; (ii) ; (iii) 5,941.5613; (iv) 16.4067 hr C) (i) 46.7341; (ii) ; (iii) 3,254.11; (iv) 11.8442 hr D) (i) 52.5141; (ii) ; (iii) 8,693.0147; (iv) 18.5179hr E) (i) 54.0741; (ii) ; (iii) 11,345.4782; (iv) 20.2973 hr ; (iii) 5,941.5613; (iv) 16.4067 hr
C) (i) 46.7341; (ii) The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours there are 135 bacteria in the culture and after 4 hours there are 390 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. ​ (i) Find the initial population. ​ (ii) Write an exponential growth model for the bacteria population. Let t represent time in hours. ​ (iii) Use the model to determine the number of bacteria after 8 hours. ​ (iv) After how many hours will the bacteria count be 25,000? ​ A) (i) 46.7341; (ii) ; (iii) 4,566.8441; (iv) 14.1787 hr B) (i) 48.8841; (ii) ; (iii) 5,941.5613; (iv) 16.4067 hr C) (i) 46.7341; (ii) ; (iii) 3,254.11; (iv) 11.8442 hr D) (i) 52.5141; (ii) ; (iii) 8,693.0147; (iv) 18.5179hr E) (i) 54.0741; (ii) ; (iii) 11,345.4782; (iv) 20.2973 hr ; (iii) 3,254.11; (iv) 11.8442 hr
D) (i) 52.5141; (ii) The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours there are 135 bacteria in the culture and after 4 hours there are 390 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. ​ (i) Find the initial population. ​ (ii) Write an exponential growth model for the bacteria population. Let t represent time in hours. ​ (iii) Use the model to determine the number of bacteria after 8 hours. ​ (iv) After how many hours will the bacteria count be 25,000? ​ A) (i) 46.7341; (ii) ; (iii) 4,566.8441; (iv) 14.1787 hr B) (i) 48.8841; (ii) ; (iii) 5,941.5613; (iv) 16.4067 hr C) (i) 46.7341; (ii) ; (iii) 3,254.11; (iv) 11.8442 hr D) (i) 52.5141; (ii) ; (iii) 8,693.0147; (iv) 18.5179hr E) (i) 54.0741; (ii) ; (iii) 11,345.4782; (iv) 20.2973 hr ; (iii) 8,693.0147; (iv) 18.5179hr
E) (i) 54.0741; (ii) The number of bacteria in a culture is increasing according to the law of exponential growth. After 2 hours there are 135 bacteria in the culture and after 4 hours there are 390 bacteria in the culture. Answer the following questions, rounding numerical answers to four decimal places. ​ (i) Find the initial population. ​ (ii) Write an exponential growth model for the bacteria population. Let t represent time in hours. ​ (iii) Use the model to determine the number of bacteria after 8 hours. ​ (iv) After how many hours will the bacteria count be 25,000? ​ A) (i) 46.7341; (ii) ; (iii) 4,566.8441; (iv) 14.1787 hr B) (i) 48.8841; (ii) ; (iii) 5,941.5613; (iv) 16.4067 hr C) (i) 46.7341; (ii) ; (iii) 3,254.11; (iv) 11.8442 hr D) (i) 52.5141; (ii) ; (iii) 8,693.0147; (iv) 18.5179hr E) (i) 54.0741; (ii) ; (iii) 11,345.4782; (iv) 20.2973 hr ; (iii) 11,345.4782; (iv) 20.2973 hr

F) B) and D)
G) A) and B)

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C

The logistic function The logistic function models the growth of a population. Determine when the population reaches one-half of the maximum carrying capacity. Round your answer to three decimal places. A) 0.402 B) 3.000 C) 0.677 D) 7.500 E) 2.000 models the growth of a population. Determine when the population reaches one-half of the maximum carrying capacity. Round your answer to three decimal places.


A) 0.402
B) 3.000
C) 0.677
D) 7.500
E) 2.000

F) None of the above
G) A) and D)

Correct Answer

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Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E) ​ Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E) ​


A) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
B) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
C) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
D) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)
E) Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. ​ ​ ​ A) B) C) D) E)

F) C) and E)
G) A) and B)

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Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ , ​ A) B) C) D) E) , Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ , ​ A) B) C) D) E) ​


A)
Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ , ​ A) B) C) D) E)
B)
Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ , ​ A) B) C) D) E)
C)
Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ , ​ A) B) C) D) E)
D)
Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ , ​ A) B) C) D) E)
E)
Use Euler's Method to make a table of values for the approximate solution of the following differential equation with specified initial value. Use 5 steps of size 0.05. ​ , ​ A) B) C) D) E)

F) C) and D)
G) D) and E)

Correct Answer

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Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E) , Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E) and when Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E) , Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E) . What is the value of Q when Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E) ? ​


A) Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E)
B) Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E)
C) Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E)
D) Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E)
E) Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four decimal places: ​ The rate of change of Q is proportional to Q. When , and when , . What is the value of Q when ? ​ A) B) C) D) E)

F) None of the above
G) B) and E)

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Each of the following graphs is from a logistic function Each of the following graphs is from a logistic function . Which one has the smallest value of b? ​ A) B) C) D) E) . Which one has the smallest value of b? ​


A) Each of the following graphs is from a logistic function . Which one has the smallest value of b? ​ A) B) C) D) E)
B) Each of the following graphs is from a logistic function . Which one has the smallest value of b? ​ A) B) C) D) E)
C) Each of the following graphs is from a logistic function . Which one has the smallest value of b? ​ A) B) C) D) E)
D) Each of the following graphs is from a logistic function . Which one has the smallest value of b? ​ A) B) C) D) E)
E) Each of the following graphs is from a logistic function . Which one has the smallest value of b? ​ A) B) C) D) E)

F) D) and E)
G) B) and D)

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E

A 300-gallon tank is half full of distilled water. At time A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 6 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 4 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places. A) lbs B) lbs C) lbs D) lbs E) lbs , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 6 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 4 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places.


A) A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 6 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 4 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places. A) lbs B) lbs C) lbs D) lbs E) lbs lbs
B) A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 6 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 4 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places. A) lbs B) lbs C) lbs D) lbs E) lbs lbs
C) A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 6 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 4 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places. A) lbs B) lbs C) lbs D) lbs E) lbs lbs
D) A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 6 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 4 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places. A) lbs B) lbs C) lbs D) lbs E) lbs lbs
E) A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 6 gallons per minute, and the well-stirred mixture is withdrawn at the rate of 4 gallons per minute. At the time the tank is full, how many pounds of concentrate will it contain? Round your answer to two decimal places. A) lbs B) lbs C) lbs D) lbs E) lbs lbs

F) B) and D)
G) A) and B)

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Use integration to find a general solution of the differential equation Use integration to find a general solution of the differential equation . ​ A) B) C) D) E) . ​


A) Use integration to find a general solution of the differential equation . ​ A) B) C) D) E)
B) Use integration to find a general solution of the differential equation . ​ A) B) C) D) E)
C) Use integration to find a general solution of the differential equation . ​ A) B) C) D) E)
D) Use integration to find a general solution of the differential equation . ​ A) B) C) D) E)
E) Use integration to find a general solution of the differential equation . ​ A) B) C) D) E)

F) B) and D)
G) A) and B)

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Find the orthogonal trajectories of the family Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E) . ​ Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E) ​


A) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E)
B) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E)
C) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E)
D) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E)
E) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E) Find the orthogonal trajectories of the family . ​ ​ A) B) C) D) E)

F) A) and B)
G) A) and E)

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