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

Eigenvalues : 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)

Asymptotic stability of a system, Continuous Time ( CT ), Time Linear-Invariant ( TLI ), CTLTI, Lyapunov Stability

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 of differential equations.

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.

Adam collects stamps.

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?

Numerical errors in a numerical solution of coupled non-linear ODEs with a linear center

NOTE: This may be more of a "non-linear dynamics" problem than an ODE one. Here goes... I've recently been toying around with this system: x' = y*e^{-(x^2+y^2)} y' = -x*e^{-(x^2+y^2)} // (where "e^" denotes the exponential function) I've noticed strange behavior that I can't seem to explain. I used a progr ...continues

Differential Equation by Separation of Variables

Could someone please help me with the problem and show me ALL the steps. (See attached file for full problem description)

Differential Equation by vseperation of Variables

Could someone please help me with the problem and show me ALL the steps. (See attached file for full problem description)

Differential Equation by Seperation of Variables

Could someone please help me with the problem and show me ALL the steps. (See attached file for full problem description)

Use any method for xy'=2y-3x

2. Use any method for xy'=2y-3x