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![12 17 101-12-1138+13] Homogeneous system (3 b) ALP ] 14-431=0 | (3] do => (+D(x-2-4=0 >$-4-6=0 *-34 +21-6=0 => j (1-3)+Q(-3)=](http://img.homeworklib.com/questions/03906ec0-aee8-11eb-88b2-07ba8c88deaf.png?x-oss-process=image/resize,w_560)
![d) X=[9] (8)et = 13-] boek 20 (57 3) a = 22 +6+3 TQ +6=-37,0 be 42–6+0 =) 49-26=0 TB + 20+40=-6 Ga=6 particulaf solution is x](http://img.homeworklib.com/questions/0404e730-aee8-11eb-8f57-3fe710f8e480.png?x-oss-process=image/resize,w_560)
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Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential...
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential...
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the syste...
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X -...
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Dete...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
O Mo Tu We Th Fr Sa Su Memo No. Date Question 4 Consider the inhomogeneous...
O Mo Tu We Th Fr Sa Su Memo No. Date Question 4 Consider the inhomogeneous clifferential equation Ä + 5x+6X = Cost - 3 Sint and the associated homogeneous differential equation X+5x+6x=0 @ Formulate the characteristic equation and solve it 6 Hence write down the general Solution of the homogeneous differential equations @ Determine values of a and b such that Xple) = a cost +6 Sint is a particular Solution of the inhomogeneous differential equaliten @ Hence write...
Consider the following system. = x + y - 2 ot dy at = 5y =...
Consider the following system. = x + y - 2 ot dy at = 5y = -2 at Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) 2= Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K = K = K = Find the general solution of the given system. (x(t), y(t), z(t)) =
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Cla...
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t)
Here is...
Consider the following non-homogeneous system of differential equations. a. Write the system in matrix form. b....
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized...
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: i = -3 with eigenvector v = and generalized eigenvector w= = [-] = [4] Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: 1 (O) = - 18.05.8:8)... y(t) B. In fundamental matrix form: (O)- x(1) y(t) [:] C. As two equations: (write "c1" and "c2" for c and c2) X(t) = yt)...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
Question 5 (Unit 6) - 31 marks (a) Express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrix form: = 2x + y + 3e", y = 4x – y. Write down, also in matrix form, the corresponding homogeneous system of equations. (b) Find the eigenvalues of the matrix of coefficients and an eigenvector corresponding to each eigenvalue. (c) Hence write down the complementary function for the system of equations. (d) Find a particular integral...
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
O Mo Tu We Th Fr Sa Su Memo No. Date Question 4 Consider the inhomogeneous clifferential equation Ä + 5x+6X = Cost - 3 Sint and the associated homogeneous differential equation X+5x+6x=0 @ Formulate the characteristic equation and solve it 6 Hence write down the general Solution of the homogeneous differential equations @ Determine values of a and b such that Xple) = a cost +6 Sint is a particular Solution of the inhomogeneous differential equaliten @ Hence write...
Consider the following system. = x + y - 2 ot dy at = 5y = -2 at Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) 2= Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K = K = K = Find the general solution of the given system. (x(t), y(t), z(t)) =
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t)
Here is...
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: i = -3 with eigenvector v = and generalized eigenvector w= = [-] = [4] Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: 1 (O) = - 18.05.8:8)... y(t) B. In fundamental matrix form: (O)- x(1) y(t) [:] C. As two equations: (write "c1" and "c2" for c and c2) X(t) = yt)...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
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