Problem 7. Consider the following system of linear differential equations: = ax + y, dt =...
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
Consider the following linear system of differential equations: dx/dt = 2x-3y dy/dt = -x +4y (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given x(0) = 3 and y(0) = 4 (d) Verify the calculations with MATLAB
Problem 4. Consider the following linear system of two equations: = 3y – ax y' = 3x – 2y. What must the relationship between a and ß be in order that the system of equations be strictly periodic.
5.[6pts] Consider the system of linear equations in x and y. ax+by = 0 x + dy = 0 (a) Under what conditions will the system have infinitely many solutions? (6) Under what conditions will the system have a unique solution? (c) Under what conditions will the system have no solution?
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
(1 point) Consider the system of differential equations dx dt = -1.6x + 0.5y, dy dt = 2.5x – 3.6y. For this system, the smaller eigenvalue is -41/10 and the larger eigenvalue is -11/10 [Note-- you may want to view a phase plane plot (right click to open in a new window).] If y' Ay is a differential equation, how would the solution curves behave? All of the solutions curves would converge towards 0. (Stable node) All of the solution...
(2-2) Problem 1, 12 points Let A and consider the system of differential 1 -2 equations y' = Ay. kx a) Find the characteristic polynomial of A b) Use the Laplace transform method to compute eAt. c) Solve the system y - Ay, 0)o
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
Problem 13.13. Consider the system of three linear differential equations: xt = 2x1 + 3x2 + 4.13 where the unknowns are the three functions xi(t), x2(t), and 23(t). x'a = 2x2 + 6.13 (a) Write the system in the form x' = Ax, where A is a (3 x 3) matrix. X'z = 2x3 (b) Write A as the sum of two matrices, A=D+U, where D is a diagonal matrix (all of the off-diagonal entries are zero, and the diagonal...
DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are proficient in DIFFERENTIAL EQUATIONS should even attempt to solve. No beginners or amateurs allowed. Please write clearly and legibly. No sloppy Handwriting. I must be able to clearly and easily read your solution and answer. Circle final answer. 9.4.3 Write the given system in the matrix form x' = Ax+f. dx = t3x-y-z+t dt dy =etz-8 dt dz dt = tx-y-10z- et Express the given system in matrix form.