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Consider the differential equation dy -0.5y (y – 4) dt Question 1 Why is the given...
Consider the differential equation dy dt = t - 2 According to the differential equation, what...
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to find the linear approximation at each of the critical...
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to find the linear approximation at each of the critical points. Determine the type and the stability. . Briefly describe the overall behavior of r and y
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...
The slope field for the equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4 is shown in the figure be...
The slope field for the
equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4
is shown in the figure below.
The slope field for the equation yxy for -4 SxS4, -4 Sy s4 is shown in the figure below TA (a) Sketch the solutions that pass through the following points: -Select The solution has slope at (0, 0) and is Concave up concave down inear (ü) (-3, 1)increasing The solution sdecreasing -Select concave up...
I need help with question #3 When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in...
I need help with question
#3
When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in years. 1. Solve for the equilibrium value(s) and determine their stability. Create a slope field for this differential equation. Use the slope field to sketch solutions for various initial values. 2. 3. Summarize the behavior of the solutions and how...
Consider the differential equation y' (t) = (y-4)(1 + y). a) Find the solutions that are...
Consider the differential equation y' (t) = (y-4)(1 + y). a) Find the solutions that are constant, for all t2 0 (the equilibrium solutions). b) In what regions are solutions increasing? Decreasing? c) Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing? d) Sketch the direction field and verify that it is consistent with parts a through c. a) The solutions are constant for (Type an equation. Use a comma to separate answers as...
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s....
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm? dy dx (b) If x+y+z-9, dt 5, and -4, find dt dz dt when (x, y, z)-(2,2,1). Problem 2. (a) Find the derivative of the function yr e-****** (b) Find the derivative of the function y - In(x* +100). cos. Problem 3. Use logarithmic differentiation to find the derivative of the function...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww +...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
hw help Consider the equation exin(y)+5x +1=y? Find dy dx in terms of X and y....
hw help
Consider the equation exin(y)+5x +1=y? Find dy dx in terms of X and y. Evaluate dx at (x,y) = (0,1). Select the correct answer. -5 5 ООО 2 Suppose that 3 xy2 = x²y + y2 + 14. dy Use implicit differentiation to find an expression for in terms of both X and y. dx dy Now give the value of when x = 3 and y = 2 dx -36 13 3 0 24 41 о ....
4. * Using your calculations from 3., plot the exact solution to dy = 1-y, dt y(0) = 1/2, for 0 <ts1, along with the numerical solution given by Euler's method and the trapezoid method, both w...
4. * Using your calculations from 3., plot the exact solution to dy = 1-y, dt y(0) = 1/2, for 0 <ts1, along with the numerical solution given by Euler's method and the trapezoid method, both with stepsize h = 0.1. Give the approximation of y(t = 1) for each numerical method. To distinguish your solutions: (i) Plot the Euler solution using crosses; do not join them with line segments. (ii) Plot the trapezoid solution using squares; again do not...
Consider the differential equation dy dt = t - 2 According to the differential equation, what is the value of y (0)? Question 3 Consider the differential equation dy dt = t - 2 and the given information y(0) = 1. Select the figure that shows the correct graphical representation of y' (O). 0 O 3 y 21 + -2 y 2 1 2 1 2 A z -1 O 3 y 2 X 2. z -1 O 3 2+...
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to find the linear approximation at each of the critical points. Determine the type and the stability. . Briefly describe the overall behavior of r and y
Consider the system given by dx/dt (1 -0.5y), dy/dx-y(2.5 1.5y +0.25 . Find the critical points . Find the Jacobian of this system and use it to...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...
The slope field for the
equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4
is shown in the figure below.
The slope field for the equation yxy for -4 SxS4, -4 Sy s4 is shown in the figure below TA (a) Sketch the solutions that pass through the following points: -Select The solution has slope at (0, 0) and is Concave up concave down inear (ü) (-3, 1)increasing The solution sdecreasing -Select concave up...
I need help with question
#3
When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in years. 1. Solve for the equilibrium value(s) and determine their stability. Create a slope field for this differential equation. Use the slope field to sketch solutions for various initial values. 2. 3. Summarize the behavior of the solutions and how...
Consider the differential equation y' (t) = (y-4)(1 + y). a) Find the solutions that are constant, for all t2 0 (the equilibrium solutions). b) In what regions are solutions increasing? Decreasing? c) Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing? d) Sketch the direction field and verify that it is consistent with parts a through c. a) The solutions are constant for (Type an equation. Use a comma to separate answers as...
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm? dy dx (b) If x+y+z-9, dt 5, and -4, find dt dz dt when (x, y, z)-(2,2,1). Problem 2. (a) Find the derivative of the function yr e-****** (b) Find the derivative of the function y - In(x* +100). cos. Problem 3. Use logarithmic differentiation to find the derivative of the function...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
hw help
Consider the equation exin(y)+5x +1=y? Find dy dx in terms of X and y. Evaluate dx at (x,y) = (0,1). Select the correct answer. -5 5 ООО 2 Suppose that 3 xy2 = x²y + y2 + 14. dy Use implicit differentiation to find an expression for in terms of both X and y. dx dy Now give the value of when x = 3 and y = 2 dx -36 13 3 0 24 41 о ....
4. * Using your calculations from 3., plot the exact solution to dy = 1-y, dt y(0) = 1/2, for 0 <ts1, along with the numerical solution given by Euler's method and the trapezoid method, both with stepsize h = 0.1. Give the approximation of y(t = 1) for each numerical method. To distinguish your solutions: (i) Plot the Euler solution using crosses; do not join them with line segments. (ii) Plot the trapezoid solution using squares; again do not...
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