7. Find and classify the type and stability of the critical point for each system below...
7 7. (20 points) Consider the system of nonlinear equations: a) The system has 4 critical points. Find them. b) One of the critical points is (-1, -1). Linearize the system at that point. c) Based on the linear system you derived in b), classify the type and stability of point (-1, -1). 7. (20 points) Consider the system of nonlinear equations: a) The system has 4 critical points. Find them. b) One of the critical points is (-1, -1)....
Find the general solution of the following system and determine the type and stability of critical point (0,0) [= [": 3] |
Please find general solution and find the type and stability of critical point (0,0) x ]' = [1 2 [x [y -5 -1] y ]
2 - 5 For each system below, (a) solve the initial value problem, and (b) determine the type and stability of the critical point at (0,0). x'= 5x - 5x2 X2' = 2xı + 3x2 xi(–117) = 7, x2(–117) = 3.
need help on number 13 Exercises 11-16. Represent each linear system in marrix form. Solve by Gauss elimination when the system is consistent and cross-check by substituting your solution set back into all equations. Interpret the solution geometrically in terms planes in R3. of 2x1 +3x2 x3 = 1 4x1 7x2+ 3 3 11. 7x1 +10x2 4x3 = 4 3x1 +3x2+x3 =-4.5 12. x1+ x2+x3 = 0.5 2x-2x2 5.0 x+2x2 3x3 1 3x1+6x2 + x3 = 13 13. 4x1 +8x2...
Consider the nonlinear system ?x′ = ln(y^2 − x) and y'=x-y-1 (a)Find all the critical points (b)Find the corresponding linearized system near the critical points. (c) Classify the (i) type (node, saddle point, · · · ), and (ii) stability of the critical points for the corresponding linearized system. (d) What conclusion can you obtain for the type and stability of the critical points for the original nonlinear system?
Consider an autonomous system , = (1 + c)x + cy where c is a real constant. (a) Calculate the trace T and the determinant of the coefficient matrix c+1 c (b) For each following cases of c, classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). Note that if a critical point is a center, it is stablhe. (4) c=흘 (2) c=-2 (1) c=-1 (3) c=-8 Consider an autonomous...
1 Find and classify the critical point(s) of the function f(x,y) = 2x2 + 3 ( (y – 2) + x(y - 1)
Question 17 Find and classify the critical point of f (, y) = 263 – 25y? – 12xy - 11x² + 46y +389. To find the critical point, you must solve two equations. Type them below: Solve this system and round your answers to the hundredths place: Find the third coordinate of the critical point: Calculate the determinant of the second-order partial derivative matrix Fill in each of the remaining spaces with a word or phrase from the following list:...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.) Consider the plane...