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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、...
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 4: 9 ptsl Suppose that a >0 and consider the initial value problem below dz 1. I2 pts] Sk...
Problem 4: 9 ptsl Suppose that a >0 and consider the initial value problem below dz 1. I2 pts] Sketch the solutions to the IVP for a-10 and a = 1 on the direction field below. Based on the direction field, does it look like the solution is defined for all real r for your choices for a? dy cos(4) II. (5 ptsl Solve the initial value problem recall that α > 0). , y(0-a. Explicitly solve for y in...
Use the direction field labeled III above to sketch the graphs of
use the direction field labeled III above to sketch the graphs
of
Use the direction field labeled III (above) to sketch the graphs of the solutions that satisfy the given initial con tions. (a) y(0) 1 (b) y(0)-2.5 (c) y(0) 3.5
Use the direction field labeled III (above) to sketch the graphs of the solutions that satisfy the given initial con tions. (a) y(0) 1 (b) y(0)-2.5 (c) y(0) 3.5
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...
1. (16) Consider the equation (a) (2) Determine all equilibrium solutions. (b) (6) Sketch a direction...
1. (16) Consider the equation (a) (2) Determine all equilibrium solutions. (b) (6) Sketch a direction field and describe the behavior of y as too if y(O) 1. (c) (8) Solve the equation exactly in explicit form.
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.)...
+0.5/1 points Previous AnswersSCalcCC4 7.2.001 2, 9x cos(Ty) is shown A direction field for the differential...
+0.5/1 points Previous AnswersSCalcCC4 7.2.001 2, 9x cos(Ty) is shown A direction field for the differential equation y y 2.0 1.5 1.0 0.5 0.4 -0.6 -0.4 -0.2 0.0 0.2 0.6 (a) Sketch the graphs of the solutions that satisfy the given initial conditions. (i) y(0) 0 (iii y(0) 1 (ii) y(0) 0.5 (iv) y(0) 1.6 V y 2:0 1.5 1.5 .5 X -0.6 O-0.6 -0.2 -0.4 0.6 -0.4 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4 2.0r 1.5 1.5 0.5...
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and...
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi stable. b) Sketch approximate but clear solutions corresponding to the initial conditions 1.0 -0.8 -0.6 -0.4 0.2 0.2 0.4 0.6 0.8 1.0 -2 .6
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi...
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...
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 4: 9 ptsl Suppose that a >0 and consider the initial value problem below dz 1. I2 pts] Sketch the solutions to the IVP for a-10 and a = 1 on the direction field below. Based on the direction field, does it look like the solution is defined for all real r for your choices for a? dy cos(4) II. (5 ptsl Solve the initial value problem recall that α > 0). , y(0-a. Explicitly solve for y in...
use the direction field labeled III above to sketch the graphs
of
Use the direction field labeled III (above) to sketch the graphs of the solutions that satisfy the given initial con tions. (a) y(0) 1 (b) y(0)-2.5 (c) y(0) 3.5
Use the direction field labeled III (above) to sketch the graphs of the solutions that satisfy the given initial con tions. (a) y(0) 1 (b) y(0)-2.5 (c) y(0) 3.5
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...
1. (16) Consider the equation (a) (2) Determine all equilibrium solutions. (b) (6) Sketch a direction field and describe the behavior of y as too if y(O) 1. (c) (8) Solve the equation exactly in explicit form.
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.)...
+0.5/1 points Previous AnswersSCalcCC4 7.2.001 2, 9x cos(Ty) is shown A direction field for the differential equation y y 2.0 1.5 1.0 0.5 0.4 -0.6 -0.4 -0.2 0.0 0.2 0.6 (a) Sketch the graphs of the solutions that satisfy the given initial conditions. (i) y(0) 0 (iii y(0) 1 (ii) y(0) 0.5 (iv) y(0) 1.6 V y 2:0 1.5 1.5 .5 X -0.6 O-0.6 -0.2 -0.4 0.6 -0.4 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4 2.0r 1.5 1.5 0.5...
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi stable. b) Sketch approximate but clear solutions corresponding to the initial conditions 1.0 -0.8 -0.6 -0.4 0.2 0.2 0.4 0.6 0.8 1.0 -2 .6
1. For the differential equation (y-y-6) șin(y/2) a) Find the critical points for y in (-6,6) and lassify the critical points as asymptotically stable, or unstable, or semi...
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...
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