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=-x+ ay where a is a constant. 1) Consider the system...
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...
plesse show work 11. For the system dr 1 1 -3 -5 31 Y , initial...
plesse show work
11. For the system dr 1 1 -3 -5 31 Y , initial condition Y, - (4,0) Write the solution and sketch the x(i) and y(1) graphs of the particular solution If the eigenvalues are of the form a + ib, b0 then determine if the origin is a spiral sink, a spiral source, or a center determine the natural period and natural frequency of of the oscillations determine the directions of the oscillations in the phase...
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)
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine...
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
Differential Questions problem. Can someone help. Thanks. 1. Consider the initial valuc problenm ay + 5y-cost,...
Differential Questions problem. Can someone help. Thanks.
1. Consider the initial valuc problenm ay + 5y-cost, y(0) = 1. Solve the IVP using THREE DIFFERENT METHODS. 2. Solve the following differential equations. If there are initial values, solve the IVP. If there are not, find the general solution. (a) (2x + y)dr + (Zy +エ)dy = 0, y(2) =-3; (o) du) dx 2y +4y 3. Solve the following initial value problems y" + 2/ + 5y = 0, y(0) =-1,...
T (1 point) Find the solution to the linear system of differential equations 8.x - 2y...
T (1 point) Find the solution to the linear system of differential equations 8.x - 2y 12x - 2y satisfying the initial conditions (0) = -5 and y(0) -13 z(t) = y(t) Note: You can earn partial credit on this problem. preview answers Entered Answer Preview
(1 point) Solving a system of linear ODEs with constant coefficients: Consider the system of equations...
(1 point) Solving a system of linear ODEs with constant coefficients: Consider the system of equations x' = 3x – 2y y = 4x – 3y = -5x + 4y + 2z, with initial conditions x(0) = 1, y(0) = 2, 2(0) = 0. The matrix of the system is 13 -20 A= | 4 -3 0 1-5 4 2) and defining the column vector r(t) X(t) = y(t) z(t) we get that X' = AX, where X(0 = 2...
Please show all work if possible, thanks! Show that the system of differential equations is Hamiltonian,...
Please show all work if possible, thanks!
Show that the system of differential equations is Hamiltonian, and find a Hamiltonian function H(x,y). You may assume that H(0,0) = 0. 3y2 - 2.c dx dt dy dt 6x2 + 2y
please show work Solve the following system. Х 0 0 +y + z = 3y +...
please show work
Solve the following system. Х 0 0 +y + z = 3y + 122 - 2y - 8z 5y + 20z 0 0 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The system has an infinite number of solutions characterized by x= y = z=r. B. The system has an infinite number of solutions characterized by x= , y=r, z=s. O C. The system has a unique...
Answer All questions please QUESTION FOUR Consider the initial value problem x(t) A(t)x(t) f(t), dt where...
Answer All questions please
QUESTION FOUR Consider the initial value problem x(t) A(t)x(t) f(t), dt where xo is some constant vector (a) Show that the associated homogenous system, x(t) A(t)x(t), has its transi tion matrix as X(t)e Ar)dr provided AeJtr)-Ar) A(t) for all t 10 Marks A(t) A(T)dr (b) Obtain a solution to the initial value problem, given that ()- () 4 A = 6 et and x(0) 1 15 Marks f(t)
QUESTION FOUR Consider the initial value problem x(t)...
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...
plesse show work
11. For the system dr 1 1 -3 -5 31 Y , initial condition Y, - (4,0) Write the solution and sketch the x(i) and y(1) graphs of the particular solution If the eigenvalues are of the form a + ib, b0 then determine if the origin is a spiral sink, a spiral source, or a center determine the natural period and natural frequency of of the oscillations determine the directions of the oscillations in the phase...
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)
dr Consider the system: = 4x – 2y dy = x + y dt (a) Determine the type of the equilibrium point at the origin. (35 points) (b) Find all straight-line solutions and draw the phase portrait for the system. (35 points) (c) What is the general solution to the system? (15 points) (d) Find the solution of the system with initial conditions: x(0) = 1 and y(0) = -1. (15 points)
Differential Questions problem. Can someone help. Thanks.
1. Consider the initial valuc problenm ay + 5y-cost, y(0) = 1. Solve the IVP using THREE DIFFERENT METHODS. 2. Solve the following differential equations. If there are initial values, solve the IVP. If there are not, find the general solution. (a) (2x + y)dr + (Zy +エ)dy = 0, y(2) =-3; (o) du) dx 2y +4y 3. Solve the following initial value problems y" + 2/ + 5y = 0, y(0) =-1,...
T (1 point) Find the solution to the linear system of differential equations 8.x - 2y 12x - 2y satisfying the initial conditions (0) = -5 and y(0) -13 z(t) = y(t) Note: You can earn partial credit on this problem. preview answers Entered Answer Preview
(1 point) Solving a system of linear ODEs with constant coefficients: Consider the system of equations x' = 3x – 2y y = 4x – 3y = -5x + 4y + 2z, with initial conditions x(0) = 1, y(0) = 2, 2(0) = 0. The matrix of the system is 13 -20 A= | 4 -3 0 1-5 4 2) and defining the column vector r(t) X(t) = y(t) z(t) we get that X' = AX, where X(0 = 2...
Please show all work if possible, thanks!
Show that the system of differential equations is Hamiltonian, and find a Hamiltonian function H(x,y). You may assume that H(0,0) = 0. 3y2 - 2.c dx dt dy dt 6x2 + 2y
please show work
Solve the following system. Х 0 0 +y + z = 3y + 122 - 2y - 8z 5y + 20z 0 0 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The system has an infinite number of solutions characterized by x= y = z=r. B. The system has an infinite number of solutions characterized by x= , y=r, z=s. O C. The system has a unique...
Answer All questions please
QUESTION FOUR Consider the initial value problem x(t) A(t)x(t) f(t), dt where xo is some constant vector (a) Show that the associated homogenous system, x(t) A(t)x(t), has its transi tion matrix as X(t)e Ar)dr provided AeJtr)-Ar) A(t) for all t 10 Marks A(t) A(T)dr (b) Obtain a solution to the initial value problem, given that ()- () 4 A = 6 et and x(0) 1 15 Marks f(t)
QUESTION FOUR Consider the initial value problem x(t)...
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