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Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of diff...
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each...
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of the given system of equation 1 +c2e2t VI The general solution is given by X (t) = ci where V2. |and 21 >A2 =| ; vi = and v2 (b) Draw a direction field and a phase portrait. Describe the behavior of the solutions as t - o. 1) If the initial condition is a multiple of...
4. Consider the system y'- Ay(t), for t > 0, with A - 1 -2 (a) Show that the matrix A has eigenva...
4. Consider the system y'- Ay(t), for t > 0, with A - 1 -2 (a) Show that the matrix A has eigenvalues וג --1and Az--3 with corresponding eigenvectors u (1,1) and u2 (1,-1) (b) Sketch the trajectory of the solution having initial vector y(0) = ul. (c) Sketch the trajectory of the solution having initial vector y(0) -u2. (d) Sketch the trajectory of the solution having initial vector y(0)-u -u 1 U
4. Consider the system y'- Ay(t), for...
please show all steps , thank you 6. Consider the initial value problem y" + 2y'...
please show all steps , thank you
6. Consider the initial value problem y" + 2y' + 2y = (t – 7); y(0) = 0, y'(0) = 1. a. Find the solution to the initial value problem. (10 points) b. Sketch a plot of the solution for t E (0,37]. (5 points) c. Describe the behavior of the solution. How is this system damped? (5 points)
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) r(0) 2, y(0)1 Determine the nullclines, sketch the vector field, and then...
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) r(0) 2, y(0)1
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.)
r(0) 2, y(0)1
PPLEASE SOLVE NUMBER 6 ONLY Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2 De...
PPLEASE SOLVE NUMBER 6 ONLY
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) 1. (0)1, y(0)0 Determine the nullclines, sketch the vector field, and then...
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) 1. (0)1, y(0)0
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) 1. (0)1, y(0)0
(a) Solve the following initial value problem: dy/dx = (y^2 − 4) / x^2 y(1) =...
(a) Solve the following initial value problem: dy/dx = (y^2 − 4) / x^2 y(1) = 0 (b) Sketch the slope field in the square −4 <x< 4,−4 <y< 4, and draw several solution curves. Mark the solution curve corresponding to your solution. (c) What is the long term behaviour of the solution from (a) as x → +∞? Is it defined for all x? (d) Find the only solution that satisfies lim(x→+∞) y(x) = 2, and explain why there...
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...
Consider the following. (A computer algebra system is recommended.) 11y' − 2y = e−πt/2, y(0) = a...
Consider the following. (A computer algebra system is recommended.) 11y' − 2y = e−πt/2, y(0) = a (b) Solve the initial value problem. y(t) = Find the critical value a0 exactly. a0 = (c) Describe the behavior of the solution corresponding to the initial value a0. For a0, the solution is y(t) =
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of the given system of equation 1 +c2e2t VI The general solution is given by X (t) = ci where V2. |and 21 >A2 =| ; vi = and v2 (b) Draw a direction field and a phase portrait. Describe the behavior of the solutions as t - o. 1) If the initial condition is a multiple of...
4. Consider the system y'- Ay(t), for t > 0, with A - 1 -2 (a) Show that the matrix A has eigenvalues וג --1and Az--3 with corresponding eigenvectors u (1,1) and u2 (1,-1) (b) Sketch the trajectory of the solution having initial vector y(0) = ul. (c) Sketch the trajectory of the solution having initial vector y(0) -u2. (d) Sketch the trajectory of the solution having initial vector y(0)-u -u 1 U
4. Consider the system y'- Ay(t), for...
please show all steps , thank you
6. Consider the initial value problem y" + 2y' + 2y = (t – 7); y(0) = 0, y'(0) = 1. a. Find the solution to the initial value problem. (10 points) b. Sketch a plot of the solution for t E (0,37]. (5 points) c. Describe the behavior of the solution. How is this system damped? (5 points)
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) r(0) 2, y(0)1
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.)
r(0) 2, y(0)1
PPLEASE SOLVE NUMBER 6 ONLY
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) 1. (0)1, y(0)0
Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) 1. (0)1, y(0)0
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...
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