Show that the zeros of two linearly dependent, nontrivial solutions of the following equation coincide. y" + A(t) y = 0

Show that the zeros of two linearly dependent, nontrivial solutions of the following equation coincide. y" + A(t) y = 0

Phase portrait

(See attached file for full problem description) --- Eigenvalues ---

Show your argument in details you can use Maple to assist you in long calculations...

(See attached file for full problem description with equations) --- Show your argument in details you can use Maple to assist you in long calculations. YOU CANNOT USE dsolve command! Consider the following system 1) Find the general solution the systems 2) Find the solution that satisfies and . Is the solution ...continues

see attachement

(See attached file for full problem description with proper equations) --- Show your argument in details you can use Maple to assist you in long calculations. YOU CANNOT USE dsolve command! Consider the following system 1) Find the general solution the systems 2) Find the solution that satisfies and . Is ...continues

Phase plain diagrams

Please solve each part of the three problems. (See attached file for full problem description)

To solve a system of Ordinary differential equations with initial conditions.

Let x: [0, infinity) -> R and y: [0, infinity) -> R be solutions to the system of differential equations: x' = - x y' = - sin y With initial condition: x(0) = y(0) = alpha, where alpha belongs to [0, pi) (a) Show that |x(t)| =< alpha for all t >= 0 (b) Show that | y(t) - ...continues

Asymptotic stability of a system.

Determine the asymptotic stability of the system x' = Ax where A is 3 x 3 matrix A = -1 1 1 0 0 1 0 0 -2 ( first row is -1 1 1 second is 0 0 1 and third is 0 0 -2) More specifically, what stability conclusion(s) can be drawn? ( Justify your answer) Please I want a detailed sol ...continues

Asymptotic stability of a system

Determine the asymptotic stability of the system x' = Ax, where A is 2x2 matrix, A = alpha beta gamma delta ( that is. first row is alpha beta, second row is gamma delta) if it is known that determinant of A, det(A) = alpha*delta - beta*gamma > 0, and th ...continues

Stability properties of zero solution to a nonlinear system

Use the function V(x,y) = x^2 + y^2 to analyze the stability properties of the zero solution of the nonlinear system x' = x + 2xy^2 y' = - 2x^2y + y More specifically, what stability conclution(s) can be drawn? ( Justify your answer) Please I want a detailed and clear solution. Thanks.

Middle school 6th grade math problem

Adam collects stamps. He has 18 bird stamps,9 flower stamps and 12 butterfly stamps. For a school project, he will display an equal number of each kind of stamp on a small poster boards. What is the greatest number of poster boards Adam can make if he uses all of the stamps?