True or False Equilibrium (0, 0) is a center of the linear system dY/dt = | 1 3   |                                                                                             |−3 2 | Y

The function of 2 variables:  f (x,y) = (5/2)x2 + 2xy - 12x + (3/2)y2 - 7y + (31/2)  Has a stationary point at (2,1). At this stationary point, the Hessian matrix for f is:  H = [5 2]        [2 3]  Which one of these options best describes the stationary point? A. The stationary point is a saddle point B. The stationary point is a local minimum C. The stationary point is a local maximum D. The nature of the stationary point cannot be determined by the Hessian matrix

Solve the linear system of the DE.

Greenvi Technical Col 4. Find a general solution of the linear system. x' = 2x + y " = x + 2y – e2t

Solve for the equilibrium points and linearize the system

Consider a system model given by d²x (t) dt² x (0) = 1 dx (t) dt - It=0 What is the free response? O 2t + 1 0 1 1 — =t = 2. -t³+2t+1 6 2t³+3t+1 + 2t

Consider a second-order nonlinear system described by i1 = x – 02, i2 = -1 – x1 + (1+x²)u, = X1 - y = x1 + 2x1x2. (a) Find all q equilibrium points xe,1, Xe,2, ..., xe,g of the system and the corresponding outputs Y0,1, Yo,2, . .. , Y0,g when the input u has a nominal value uo = 1. (b) For each i E {1,2, ..., q}, linearize the system around the operating point (xe,i, u0, Yo,i).

Find and classify the critical point of the linear system. dx/dt = -3x-y-19 dy/dt = 13x+y+69

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