For each of the regions, determine the direction of the vector field associated to our system of linear differential equations. You have four choices. Region Direction of the vector field || Right up | --| Left down || 1 Left up || Right down Right downLefp Right up Left down 0 || Right up || ︶ Right down || 0 || Left up ||。11 Left down Left down eft up Right up Right down
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Consider the system of linear differential equations z,(t)-17/11 z(t) + 9/11 y(t) y,(t)-18/11 z(t...
Consider a system of differential equations describing the progress of a disease in a population,...
Consider a system of differential equations describing the progress of a disease in a population, given byF, ) for a vector-valued function F. In our particular case, this IS. where z(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y 2/3 The...
3. Consider the system of differential equations = z+9-1 (a) Sketch the r-nullcline, where soluti...
just (A) (B) (C)
3. Consider the system of differential equations = z+9-1 (a) Sketch the r-nullcline, where solutions must travel vertically. Identify the regions (b) On a separate set of axes, sketch the y-nullcline, where solutions must travel horizon in the plane where solutions will move toward the right, and where solutions move toward the right tally. Identify the regions in the plane where solutions will move upward, and where solutions move downward. (c) On a third set of...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. and =...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 where x(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of...
5. Consider the system of differential equations regarding x = c(t), y = y(t), and z...
5. Consider the system of differential equations regarding x = c(t), y = y(t), and z = z(t): x' = 211 x + 212 y + 213 2 y = 221 x + 222 y + 223 2 z' = 231 2 + 232 y + 233 z where 211, 212,..., 233 are all real constants. Which of the following options could be a general solution of this system? (a) C C[-] é 2t + C2 eft (b) C-1 137...
Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x), taking (x,y)>0. (1 point) Consider the system of equations...
Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x),
taking (x,y)>0.
(1 point) Consider the system of equations de = 2(3 – 2 – 49) = y(1 - 33), taking (2,y) > 0. (a) Write an equation for the (non-zero) vertical (-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: (Enter your equation, e.g. y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria =...
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines....
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines.
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
(1 point) Consider the system of higher order differential equations 2 Rewrite the given system o...
(1 point) Consider the system of higher order differential equations 2 Rewrite the given system of two second order differential equations as a system of four first order linear differential equations of the formy - P(t)y + g(t). Use the following change of variables y (t) y2(t)y'(t) 3 (t) y(t) у(t) z(t) -y2 4
(1 point) Consider the system of higher order differential equations 2 Rewrite the given system of two second order differential equations as a system of four...
Differential Equations 11. Which ordinary differential equation below is equivalent to the following system of linear...
Differential Equations
11. Which ordinary differential equation below is equivalent to the following system of linear equations? = -12 t = 3.81 - 12 + cos(t) (a) u" - 3u' +u = cos(t) (b) " +34 +u = -cos(t) (c) " + u' + 3u = -cos(t) (d) " + x - 3u = cos(t)
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutio...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
Consider a system of differential equations describing the progress of a disease in a population, given byF, ) for a vector-valued function F. In our particular case, this IS. where z(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y 2/3 The...
just (A) (B) (C)
3. Consider the system of differential equations = z+9-1 (a) Sketch the r-nullcline, where solutions must travel vertically. Identify the regions (b) On a separate set of axes, sketch the y-nullcline, where solutions must travel horizon in the plane where solutions will move toward the right, and where solutions move toward the right tally. Identify the regions in the plane where solutions will move upward, and where solutions move downward. (c) On a third set of...
(3) - F(2,4) to Consider a system of differential equations describing the progress of a disease in a population, given by for a vector-valued function F. In our particular case, this is: t' = 3 – 3zy - 12 y' – 3ay – 2y where I (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. and =...
Assignment 8 Remaining Time: 131:53:22 Question 1 Consider a system of differential equations describing the progress of a disease in a population, given by F(x, y) for 1 point How Did I Do? a vector-valued function F. In our particular case, this is: d' = 3 – 3xy - 12 y' = 3xy – 34 where x(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of...
5. Consider the system of differential equations regarding x = c(t), y = y(t), and z = z(t): x' = 211 x + 212 y + 213 2 y = 221 x + 222 y + 223 2 z' = 231 2 + 232 y + 233 z where 211, 212,..., 233 are all real constants. Which of the following options could be a general solution of this system? (a) C C[-] é 2t + C2 eft (b) C-1 137...
Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x),
taking (x,y)>0.
(1 point) Consider the system of equations de = 2(3 – 2 – 49) = y(1 - 33), taking (2,y) > 0. (a) Write an equation for the (non-zero) vertical (-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: (Enter your equation, e.g. y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria =...
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines.
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
(1 point) Consider the system of higher order differential equations 2 Rewrite the given system of two second order differential equations as a system of four first order linear differential equations of the formy - P(t)y + g(t). Use the following change of variables y (t) y2(t)y'(t) 3 (t) y(t) у(t) z(t) -y2 4
(1 point) Consider the system of higher order differential equations 2 Rewrite the given system of two second order differential equations as a system of four...
Differential Equations
11. Which ordinary differential equation below is equivalent to the following system of linear equations? = -12 t = 3.81 - 12 + cos(t) (a) u" - 3u' +u = cos(t) (b) " +34 +u = -cos(t) (c) " + u' + 3u = -cos(t) (d) " + x - 3u = cos(t)
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
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