4. For the systems *=x-xy y=y-giả 3 = -4y + 2xy-8 y = 4y² = x² find all equilibria. Linearize at every equilibrium, find stable/unstable spaces for the linearized systems, and sketch the phase portrait of the linear flow. By the Stable Manifold Theorem the nonlinear flow is a small distortion of the linear if one stays close to the equilibrium.

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

A: Given that, A system of the type x˙=fx, fx=-grad Vx is called a gradient system.  Investigate the…

Q: fx=å (3in (x*ry)-x2) %3D fy = Ly(31n (x*+y)-x2) %3D d fe-(3in (x*ry)-x2)

A:

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: 2. The behavior of the system is a saddle. x' = − x+y, |y' = − x − y -

A: (.) Given system is,                   We write the given system in matrix form,

Q: 2. The behavior of the system is a saddle. x' = -x +y, y = -x-y

A: The given system of differential equations is:…

Q: onsider the following equation system: (P =r – Q – I+w P= α + Q | I = BQ + Vw here Q,P,I are the…

A:

Q: Q/ If the equilibrium point is the origin of the nonlinear system, then the Libanov function can be…

A: Given,Condition about " Libanov function" to check the stability of the non-linear system.

Q: Find the equilibrium point. D(x) = 7- 8x, S(x) = 3 + 8x

A: Equilibrium point is the point at which demand and supply function intersects. That means at…

Q: Consider the equ dS = (1-P)r - BCS ty C - S dt dc = pcs dt. d I dt. • SCIR disease type model pcs -…

A:

Q: Draw nullclines and Phase portraits and specify the type of equilibrium points using phase…

A: Given: x'=x+2yy'=-5x-y To find: Points

Q: Find all equilibrium points and determine their types when C =1. *, = x2 *, = -bx, +1+ c(-1+ sat…

A: Given: x.1=x2x.2 =-bx2+1+c-1+sat0.5-x1-x2

Q: Is it possible for a non-autonomous equation = f(x,y) to have an equilibrium (i.e.: constant)? If…

A: Is it possible for a non-autonomous equation dy/dx = f(x,y) to have an equilibriumsolution y = yo…

Q: Let 5xyz = e².

A:

Q: Find all the first partial derivatives of z = 5a y-8y. (Choose all applicable answers.) O z = 40x'y-…

A:

Q: Use the Chain Rule to find the indicated partial derivatives x = s + 2t - u, y = stu²; when s = 4, t…

A:

Q: Linearize the nonlinear equation f(r,y) = r + 8.ry + y in the region defined by 2 <r < 4, 10 <y <…

A: The Linearization of a function f(x,y) at a point (a,b) is L(x,y) = f(a,b)+(x-a)fx(a,b)+(y-b)fy(a,b)…

Q: 4. Find the four second partial derivatives for f(x,y) = x²sin y. state final answers and show all…

A: NOTE: Refresh your page if you can't see any equations..Take the partial derivative with respect to…

Q: Let 3x² - 7xy + 2y²+x-12y-14=0. Use partial derivatives to calculate dy dz (-2,1) TE at the point…

A: First of all, we will differentiate then we will put the values of x and y

Q: 4) Find all first-order partial derivatives w = f(x,y, z) = 2x³y³ – /xyz + 4z6x y3

A:

Q: Find the indicated partial derivatives of: at the point (x, y) = (2, 4). of (2,4) = 8/81 (2,4)= | ||…

A:

Q: A culture of yeast grows at a rate proportional to its size. If the initial population is 8000 cells…

A: I have written everything with in the solution. Please go through that.

Q: Find the partial derivatives of the function with respect to each variable.

A:

Q: y(o)=-3,5'(0 こ 4X と 5ン=35e

A:

Q: 3. Use method of undetermined coefficients 2X y" - 4y = 8xe

A:

Q: af af Use the Chain Rule to evaluate the partial derivatives and at (u, v)= (-3,-3). ди ди f(x, y,…

A: We have  fx,y,z=x3+yz2x=u2+vy=u+v2z=3uv Now,…