dx = x³ — y³, dy = 2xy² + 4x²y + 2y³. dt dt Construct a Lyapunov function of the form V(x, y) = ax²+ cy², where a and c are to be determined, to show that the single critical point of the system at the origin is unstable.

Q: consider the nonlinear second-order ODE x''+2x'+4x/(1+x^2)=0 a. convert to DE to a system b. Find…

A: Given: The nonlinear second-order ODE is

Q: Consider any(n) + an-1y(n-1) + + a1y' + aoy = f(x) where an, ...a1, ao E R, where an 7 0. ... (a)…

A: consider anyn+an-1yn-1+.....+a1y'+a0y=fx            ...i where an, ......., a1 , a0∈ℝ where an≠0 (a)…

Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: An image is projected onto a wall, and the irradiance of the light on the wall is (3) given by f(x,…

A:

Q: d.S dt dI dt = TI - PSI, pSI – TI, where I represents individuals who are infected with some virus…

A: The system of differential equations given describes a simplified model of disease spread.The…

Q: æ'(t) = x · (1 – a²), y'(t) = -y*

A: Now our first goal is to calculate the equilibrium point, so that we equate the given system of…

Q: Consider the disease epidemics model from assignment 9, d.S rI - PSI, dt dI dt pSI - TI, where I…

A: Given that:Consider the disease epidemics model from assignment   where I represents individuals who…

Q: The system dx/dt = x + y, dy/dt = x + 2y + 1 has a constant solution. true or false?

A: dx/dt = x + y,dy/dt = x + 2y + 1

Q: Consider the system x ' - x = u ( t ) . Can one steer 1 to 0 by a differentiable control function u…

A: Yes, it is possible to steer the state variable (x) from 1 to 0 by choosing an appropriate…

Q: Consider the system of equations a' = µx + y – x(x² + y³), y' = -x + µy – y(x² + y³),

A:

Q: Find a family of functions z=f(x,y) whose partial derivatives are given, or explain why this is…

A:

Q: The nonlinear system has a critical point at (0,0). dx/dt = -x dy/dt = -(4x^3) + y find the…

A:

Q: Consider the function y²x² y² + x² 0 if (x, y) = (0,0) if (x, y) = (0,0) Compute the partial…

A:

Q: 3.Consider the system dx/dt=6x-2x^2-xy dy/dt=6y-2y^2-xy a. Find and classify all critical points

A: Set dxdt=06x-2x2-xy=0x6-2x-y=0x=0 or x=3-y2

Q: True or False The system dx/dt = 2y dy/dt = sin(xy) has only one equilibrium point.

A: We need to equate both the derivative to 0, to calculate the equilibrium points.

Q: The function u(x, y) satisfies the partial differential equation J²u J²u xy- əx² дхду +x². ди Y əx…

A:

Q: x' 3D За — 2у + e"siny 4х — у +е Vsin x

A: In this question,  we find the linearization of this system near the critical point (0,0) by using…

Q: 8. Consider the given nonlinear system of differential equations: x' = 60x – 3x – 4xy, = 42y – 3y –…

A: Given that the nonlinear system of differential equations x'=60x -3x2-4xy, y1 = 42y - 3y2 -2xy has a…