5: For the following system, (a) provide the general solution, (b) provide a sketch showing the q...
sor the following system, (a) provide the general solution, (b) 3: a tive properties of the system, (c) specify what type (spiral) source/sink, center, saddle) of provide a sketch showing, the ualitati quaibrium point the origin is. You should include any straight-line solutiona as well as indicate eq eneral types of solution curves. Be sure to indicate the direction of motion along any solution curve. dY (-5 dt42)
5. A general solution of x' Ax is given by (a) G Sketch the half-line solutions g h the half-line solutions generated by each exponential term of the solution. Then, rough approximation of a solution in each region determined by the half-line solu- sketch a tions . Use arrows to indicate the direction of motion on all solutions. -2 The equilibrium at the origin is best classified as a (circle one): i. nodal sink, ii. nodal source (b) v. spiral...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution. ar dY (1 -3 dt Y, Problem 3. For the...
2 Y, Y(t) 2 dY 5. For the system dt - 2. a) Write the general solution. b) State if the origin is a spiral sink, or a source, or a center. c) Write the natural period and the natural frequency of the solutions. d) Do the solutions go clockwise or anti clockwise around the origin? (0) e) Write the particular solution that corresponds to ly(0) =
For the system: a. Write the general solution b. State if the origin is a spiral sink, source, or center and explain why. c. Write the natural period and natural frequency of the solutions. d. Do the solutions go clockwise or anticlockwise around the origin? Explain your reasoning. e. Write the particular solution that corresponds to Please write clearly and explain your steps. Thank you! Do not just copy someone else's answer.
-5 2 1 a. Find the most general real-valued solution to the linear system of differential equations z' do o 0 xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle O center point / ellipses spiral source spiral sink none of these
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution dY (1 -2
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
a Find the most general real-valued solution to the linear system of differential equations a' -3 -4 -3 21(t) + 22(t) b. In the phase plane, this system is best described as a O source / unstable node O sink/stable node O saddle center point / ellipses spiral source spiral sink none of these
Problem 8. 1 point) a. Find the most general real-valued solution to the linear system of differential equations x (1) C: + C2 x2 (1) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these