Analyze the stability of the critical point of the following system, proposing as a Lyapunov function V(x,y)=ax2m+by2n. a) x′=−2xy, y′=x2−y3

Q: g(y) y - 1 y²y + 1 2

A: to find critical points of gy=y-1y2-y+1

Q: Ury is 10. (i) Show the general solution of the PDE u(x, y) = F(x) + G(y) for arbitrary functions F,…

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Q: The general solution to y'' - xy' + y = 0 is given by:

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Q: Calculate the partial derivatives af/ax and afƒ/ay of each function: (i) f(x,y) = (2x - 3y)². (ii)…

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Q: This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: By eliminating the arbitrary constants of y = Gx + C2x² through isolation, then which of the…

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Q: 10. Consider the linear regression model with assumptions (i) to (iii) and (iv*) with V = k? I, + V1…

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Q: The critical Points of f (x, y) = x³ – 3x + 3y² – 6y are:

A: The critical points of a function f(x, y) can be obtained by solving the partial derivatives ∂f∂x=0…

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let (x, Y,) be the solution of the following equations (2x)" = (3y)m3 3Inx = 2lny In 2 %3| %3D Then…

A: Introduction :

Q: y" + 3y' + 2y = 12x²; y(0) = a, y'(0) = b

A: Follow the steps below.

Q: Find all the second order partial derivatives of the given function. 10) f(x, y) = (x2 + y2)7

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Q: 3 L[y] =y' --y is a linear operator. If u(x) = −4x² + 2x, then find L[u(x)]. X a) -4x² - 6x b) -…

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Q: The solution to the IVP (x² + y²) y'+xy=0 with y (0) = 2 is y (2x²-y)=4. y²(2x² + y²) = 16. Oy²(2x²…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: 3. Find the critical points of if(x,y) = x²+x-3xy + y³-5, Use the second partial derivative test to…

A: Step 1:Step 2:Step 3:

Q: If Var(X+Y)=5, Var(X-Y)=2 and E(X)=1 and E(Y)=2 then Cov(X,Y)= (3/4 (1/4 (4/B

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If (1,1) is a critical point of f(x,y) = x³ – 3x + 3y² – 6y then (1,1) is:

A: (1,1) is the local minimum point   explanation is given in below step

Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: f(x,y)=x2+4xy we have to find the critical points.

Q: (c) Consider the double integral || xy dA where D is bounded by the x-axis and the upper half…

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Q: The demand and supply functions for three (03) goods are given as follows: Dx = 100-3Px+Py+3Pz Dy…

A: The equilibrium point is the point where demand function is equal to the  supply function. Thus,…

Q: x²y" − 3xy' + 4y = 0 - a) b) c) d) e) which of the following is the general solution of the equation…

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Q: Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) +…

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Q: For each of the following systems, find all the equilibrium points x₁ = x₂ a) (x₂ =−x₁ - x₂ + ² -X1…

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Q: Consider the equation y" + ay' + by = f(x) the constants a and b are real and different from zero,…

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Q: Find the maximum value of f(x1,2,,xn) = (x₁ - x₂ ... n)¹/" where x₁,..., In are positive numbers and…

A: (a) Maximize?(?1,?2,...,??)=?1?2...??n subject tog(x1,x2,...,xn)=x1+x2+.........+xn=cand xi>0By…

Q: Check if the system with the following input-output relation are i) Memory/memory less ii) Causal…

A: a) Here, the relation is, yt=x4t+xt-3.