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1. For each of the following systems, (i) determine all critical points, (ii) determine the corresponding...
#10 all parts In each of Problems 5 through 18: (a) Determine all critical points of the given system of equations. (b) Find the corresponding linear system near each critical point. (c) Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system? (d) Draw a phase portrait of the nonlinear system to confirm your conclusions or to extend them in those cases where the linear system does not provide definite information about the...
Consider the nonlinear System of differential equations di dt dt (a) Determine all critical points of the system (b) For each critical point with nonnegative x value (20) i. Determine the linearised system and discuss whether it can be used to approximate the ii. For each critical point where the approximation is valid, determine the general solution of iii. Sketch by hand the phase portrait of each linearised system where the approximation behaviour of the non-linear system the linearised system...
1.7-1 For the systems described by the equations below, with the input f(t) and output v(t), determine which of the systems are linear and which are nonlinear. dy dt (a) + 2y(t)-f(t) (b) +3y() -se) (e) ( ) +2y(t)-f(t) (d) +92(t) = f(t) (c) 3y(t) + 2 = f(t) (f) + (sin t)y(t)-2 + 2/(t) dt dt (h) v(t)f(r)dr dt
Problem 5. Consider the system = I-? – ry, = 3y - xy - 2y? Please answer the following questions. (a) Determine all critical points of the system of equations. (b) Find the corresponding linear system near each critical point. (c) Discuss the stability of each critical point for the nonlinear system.
1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system. 185 Exercises (b) Describe the phase portrait for the nonlinear system (c) Does the linearized system accurately describe the local bchavior near the equilibrium points? (iii) x' = x+ y, y, 2y 1. For each of the following nonlinear systems, (a) Find all of the equilibrium points and describe the behavior of the associated linearized system....
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 the given system di = 2x²y – 3x2 - 25 y, y=-2xy? + bxy. x Incorrect (a) Determine all critical points of the given system of equations. Write your points in ascending order of their x-coordinates: if two points have the same x-coordinate, write them in ascending order of (x2.72) =( x Incorrect. (b) Find the corresponding linear system near each critical point. 1. The linear system near the critical point ($1.91) () = A (s) where: 1. The...
1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b) ( dy + (c) sin t (d) (1y) sin t ( cos2 t 1 y sin(t)= 0 (e) Int +3etdy dt (f) 2y'-y2 =e (g) y"(t2 1)y+cos(t (h) y"sin(ty)y(t21)y 0 = 0 1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b)...
2. Consider the nonlinear autonomous system of DEs: dx dt dy dt (a) Find all critical points of this system. (Make sure that you have found all of them.) (b) Find the linearization (a linear system) at each critical point. Calculate the eigen- values of the contant coefficient matrix, classify the corresponding critical point, and state its stability.
MTH 295 Homework set # 7 The following problems will be fully graded with the possibility of earning partial credit. To receive any credit, you must show a sufficient amount of work when applicable. If you use additional paper to show your work, insert the additional work sheets between the test pages. DO NOT staple. Sloppy, haphazard work will not receive credit. Give the answers in the spaces provided, and the work on separate sheets of paper. Consider the following...