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1. (16) Consider the equation (a) (2) Determine all equilibrium solutions. (b) (6) Sketch a direction...
Given the equation y' 9-16y, a) Find all Equilibrium solutions b) Determine whether each solution is...
Given the equation y' 9-16y, a) Find all Equilibrium solutions b) Determine whether each solution is stable, unstable or neither. c) Sketch the direction field.
Given the equation y' 9-16y, a) Find all Equilibrium solutions b) Determine whether each solution is stable, unstable or neither. c) Sketch the direction field.
8. Consider the autonomous DE: y y+1)(y- 2) a) Find and sketch below the equilibrium solutions....
8. Consider the autonomous DE: y y+1)(y- 2) a) Find and sketch below the equilibrium solutions. b) Find the region where the solutions are increasing c) Draw the direction field. d) Sketch three solutions passing respectively through the points (0, 0), (0, 3) and (0, -2) (15 4 2. 0 2 4 2 -2 4
8. Consider the autonomous DE: y y+1)(y- 2) a) Find and sketch below the equilibrium solutions. b) Find the region where the solutions are increasing...
consider the autonomous equation 2. Consider the autonomous equation y=-(y2-6y-8) (a) Use the isocline method to ske...
consider the autonomous equation
2. Consider the autonomous equation y=-(y2-6y-8) (a) Use the isocline method to sketch a direction field for the equation (b) Sketch the solution curves corresponding to the following intitial conditions: (1) y(0) 1 (2) y(0) =3 (3) y(0)=5 (4) 3y(0) 2 (5) y(0) = 4 (c) What are equilibrium solutions, and classify its equilibrium them as: sink (stable), source, node. (d) What is limy(t) if y(0) = 6? too
2. Consider the autonomous equation y=-(y2-6y-8) (a)...
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...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are constant, for all t20 (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 needed.)...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are constant, for all t20 (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 needed.)...
2. (6 points) A direction field for a difrential equation is showa below. Sketch the grphs of the solutions that satisfy the following initial conditions: (a) y(-1-1) (b) y(4)=-2 (e) y(2)=0 111、...
2. (6 points) A direction field for a difrential equation is showa below. Sketch the grphs of the solutions that satisfy the following initial conditions: (a) y(-1-1) (b) y(4)=-2 (e) y(2)=0 111、 tITIIITI withII this, but it shouldn't look like Pollock. AIYITTIIIAII
2. (6 points) A direction field for a difrential equation is showa below. Sketch the grphs of the solutions that satisfy the following initial conditions: (a) y(-1-1) (b) y(4)=-2 (e) y(2)=0 111、 tITIIITI withII this, but it shouldn't...
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s)....
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s). b) Create an appropriate table of values and then sketch (using the grid provided) a direction field for this differential equation on OSIS 3. Be sure to label values on your axes. c) Using the direction field, describe in detail the behavior of y ast approaches infinity. 2. Short answer: State whether or not the differential equation is linear. If it is linear, state...
2. Differential equations and direction fields (a) Find the general solution to the differential equation y'...
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation...
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability of the equilibria you found in (a). (c) How does the solution with y(0) =-1 behave as t -» +00? How does the solution with y(0) 1 behave as t - --0?
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability...
Given the equation y' 9-16y, a) Find all Equilibrium solutions b) Determine whether each solution is stable, unstable or neither. c) Sketch the direction field.
Given the equation y' 9-16y, a) Find all Equilibrium solutions b) Determine whether each solution is stable, unstable or neither. c) Sketch the direction field.
8. Consider the autonomous DE: y y+1)(y- 2) a) Find and sketch below the equilibrium solutions. b) Find the region where the solutions are increasing c) Draw the direction field. d) Sketch three solutions passing respectively through the points (0, 0), (0, 3) and (0, -2) (15 4 2. 0 2 4 2 -2 4
8. Consider the autonomous DE: y y+1)(y- 2) a) Find and sketch below the equilibrium solutions. b) Find the region where the solutions are increasing...
consider the autonomous equation
2. Consider the autonomous equation y=-(y2-6y-8) (a) Use the isocline method to sketch a direction field for the equation (b) Sketch the solution curves corresponding to the following intitial conditions: (1) y(0) 1 (2) y(0) =3 (3) y(0)=5 (4) 3y(0) 2 (5) y(0) = 4 (c) What are equilibrium solutions, and classify its equilibrium them as: sink (stable), source, node. (d) What is limy(t) if y(0) = 6? too
2. Consider the autonomous equation y=-(y2-6y-8) (a)...
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...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are constant, for all t20 (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 needed.)...
Consider the differential equation y' (t) = (y-2)(1 + y). a) Find the solutions that are constant, for all t20 (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 needed.)...
2. (6 points) A direction field for a difrential equation is showa below. Sketch the grphs of the solutions that satisfy the following initial conditions: (a) y(-1-1) (b) y(4)=-2 (e) y(2)=0 111、 tITIIITI withII this, but it shouldn't look like Pollock. AIYITTIIIAII
2. (6 points) A direction field for a difrential equation is showa below. Sketch the grphs of the solutions that satisfy the following initial conditions: (a) y(-1-1) (b) y(4)=-2 (e) y(2)=0 111、 tITIIITI withII this, but it shouldn't...
1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s). b) Create an appropriate table of values and then sketch (using the grid provided) a direction field for this differential equation on OSIS 3. Be sure to label values on your axes. c) Using the direction field, describe in detail the behavior of y ast approaches infinity. 2. Short answer: State whether or not the differential equation is linear. If it is linear, state...
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability of the equilibria you found in (a). (c) How does the solution with y(0) =-1 behave as t -» +00? How does the solution with y(0) 1 behave as t - --0?
3. [20 pts.] (a) Find the equilibrium solutions of the equation y-υw-2)3. (b) Sketch the phase line of the equation, and determine the stability...
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