Let   dx/dt =   x2y3           dy/dt  = -x - y - (xy4)/2 be a dynamical system.   Is  L(x,y) = (x2)/2 + (x2y4)/4 a proper Lyapunov function

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Q: 5c) Find the partial derivatives?     y = 2x2+3xz+85w-8z2

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Q: A system of the type i = f(x), f(x) = -gradV(x), is called a gradient system. Investigate the…

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Q: Part II: Find the first partial derivatives of the given functions. z = (y/x³)(x/y³) ENTIA EDIA…

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Q: Find the first order partial derivatives of: (a) g(x1, x2) = (3x1 + 2x2) 5. Ans: f1=? f2=? (b)…

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Q: Both first partial derivatives of the function f(x.y) are zero at the given points. Use the…

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Q: = 0. c) y(0) = 1, y'(0) = 0, y"(0) = -1. Is the set of functions linearly independent or linearly…

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Q: a) Suppose you are given model with two explanatory variables such that: Y₁ = a + B₁x₁i + B₂x₂₁x +…

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Q: Give an example of ANY one nonlinear (i.e. powers of r, y can't just be 1) function z f(r, y) such…

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Q: Which of the following functions V(y1, y2) is a Lyapunov function for the dynamical system y₁ =…

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Q: Solve Fyy + 3 Fxy + 2 Fxx = 2x, F(x, 0) = -x, 2, F(x, 0) = 0. F(x, y) =

A: General solution is given by complementary factor + particular integral.

Q: nt) Consider the discrete-time dynamical system x1+1 = 4x,(1-x₂). If x₁ = ₁, X1+1 = Is x = an…

A: see my solution below

Q: What is the stability of equilibrium points of A and B? Is the energy of B higher than A?

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Q: ht) Consider the discrete-time dynamical system Xr+1 - What is the equilibrium for this system? What…

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Q: In substituting the point (4,1,2) in the partial derivatives, why does the terms without x and y…

A: In part (2), we have the following: ∂g∂x4,1,2=-π1 sin4π -14-1 ln3log332 Now, sin4π=0 So,…

Q: 10.J Compute the matrix of partial derivatives of: f(x,y) = (x+y, x-y, xy) d.) f(x, y, z) =…

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Q: Assume that  dx1/dt= x1(2-x1)-x1x2 dx2/dt= x1x2-x2 a) Graph the zero isoclines. b) Show that (1,…

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Q: Find the partial derivatives W = Əw Әх Əw ду х2 +y2 х2 - уг = II - 4xy2 (x² - y²)² 2 2 4xy2 (x²-₁²)²…

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Q: (xey-1) Q2: Let f (x, y) = Compute all first and second partial derivatives. (yex-1)'

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