Show that if a two-dimensional (nonlinear) mass-action system has a globally attracting compact set within the strictly positive quadrant, then it is persistent and it is also permanent.

Show that if a two-dimensional (nonlinear) mass-action system has a globally attracting compact set within the strictly positive quadrant, then it is persistent and it is also permanent.

solve the differential equation

Solve the following systems of initial-value problems using the Laplace transform method: x'1 - 3x'2 + 4x1 - 5x2 = 0 , x'2 - x'1 + 3x2 = 5 , x1(0) = 0 , x2(0) = 0

Solve the following initial-value problem using Laplace transforms. y''- y' - 2y = 5sin(x) ; y(0) = 1 , y'(0) = -1

Find the Laplace transform of the following function. Fa(t) = {t/a for t < a, where a >(or equal to)...

Dear expert, kindly suggest how to solve a second order differential equation by transforming it into Bessels' differential equation using a given substitution. Eg solve: xy''+y'+y/4=0...

Given $\frac{\partial x}{\partial t}+x^3=yx^2$, $x(0)=x_{0}$, where $x$ : $\mathbb{R}^+ \mapsto \mathbb{R}$ and $y$ : $\mathbb{R}^+ \mapsto \mathbb{R} $ with $\int_{0}^{t} y^2(s) ds <...

Find the general solution to tln(t)dr/dt+r=7te^t I used integrating factor to solve it and found the answer= C/lnt+7e^t/lnt but it's wrong?

Put the differential equation ty'/(t^3+7)y=cos(t)+(e^(5t))/y into the form y'+p(t)y=g(t) find p(t) find g(t)

I've been trying to solve this problem for hours. Find the solution of the differential equation (ln(y))^4 dy/dx=x^4*y which satisfies the initial condition y(1)=e^2 y=...

How would I write this in matrix form (x' = AX) x' = x y' = y Note: Is it supposed to be like this: x' = (1 v 1)(x v y) or x' = (1 + 0 v 1 + 0)(x v...

Find the derivatives of each of the following vectors. x(t) = [ t3 - 2t2 +t etsin(t) ]

dy/dx =( xsquare + y + 1 ) whole square

Determine the specific solution of the following initial-value problems. Use the method of undetermined coefficients to find the particular solution. y'' - 2y' + 2y = x3 - 5, y(0)=6 and...

Using the method of undetermined coefficients, determine the general solution of the following second-order, linear, non-homogenous equations. y'' - 2y' + 2y = sin(x) + cos...

Using the method of undetermined coefficients, determine the general solution of the following second-order, linear, non-homogenous equation. y''- 4y' + 4y = 2e2x+3 note:...

Determine the specific solution of the following initial-value problems. y''-6y'+9y=0, y(-2)=1 and y'(-2)=0

The supply equation for a certain brand of radio is given as follows where x is the quantity supplied and p is the unit price in dollars. p = s(x) = 0.3√x + 15 Use differentials to approximate...

A coat of paint of thickness 0.06 cm is to be applied uniformly to the faces of a cube of edge 32 cm. Use differentials to find the approximate amount of paint required for the job, correct to the...

Use differentials to approximate the quantity a. √101 b. 4√81.6