PLEASE HELP! 1. Consider the equation d2x dt2 (a) (b) (c) (d) Find a conserved quantity...
(1 point) If the differential equation d2x dt2 . dx + 6- m + 3x = 0 dt is overdamped, the range of values for m is? (inf,3) Your answer will be an interval of numbers given in the form (1,2), (1,2), (-inf,6), etc. (1 point) Write the given second order equation as its equivalent system of first order equations. u" + 3 + 7u = 0 Use v to represent the "velocity function", i.e. V = u(t). Use v...
PLEASE HELP !!!! thanks 14. 12 points! The phase portrait (without arrows) of a non-linear syster dz 3-32, 16r dt 2 dy dt a) Mark all critical points directly on the 2 diagram, and classify them using only the fact that this is a Hamiltonian system. -2 b) Find a Hamitonian function (or conserved quantity) H(,u) whose level curves include the curves shown above. 14. 12 points! The phase portrait (without arrows) of a non-linear syster dz 3-32, 16r dt...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
4. (a) Write the corresponding first-order system, (b) find the eigenvalues and eigenvectors, (c) classify the oscillator and, when appropriate, give the natural period, and (d) sketch the phase portrait. dt dt 4. (a) Write the corresponding first-order system, (b) find the eigenvalues and eigenvectors, (c) classify the oscillator and, when appropriate, give the natural period, and (d) sketch the phase portrait. dt dt
consider the system of differential equations ; 1) Find the fixed points of the system , 2) Evaluate the Jacobian Matrix at each fixed point, 3) Classify stability of each fixed point, 4) Sketch the graph of the phase portrait,
1. Consider the system 2(t)--3i(t) +z2(t) +3() (a) (i) Find the linearised system at the equilibrium point (0, 0). (ii) What type of equilibrium point is (0,0)? (State your reasons fully.) (ii) Sketch the phase portrait for the linearised system near (0,0). (b) Repeat part (a) for the equilibrium point at (1,0). (c) (i) Are there any other equilibria? (ii) Read the Grobman-Hartman theorem and confirm that it applies to the above equilibria. 1. Consider the system 2(t)--3i(t) +z2(t) +3()...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
I need help with this question of Differential Equation. Thanks Find and classify the equilibrium solutions and sketch the phase plane of the following system of ordinary differential equations. fx' = y(x - 1) y = x(y + 1)
help please asap Page 7 pulmts) A disease outbreak shows a rate of infection given by the differential equation dI e21-3(13- 12-421), dt for t measured in days and I(t) representing the number of infected individuals (in hundreds) at time t. Answer the questions below, showing all work and putting a box around your final answer. (a) (3 points) Find the biologically relevant equilibria of this differential equation. (b) (3 points) State the relevant stability theorem and use it to...