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(3 points) Given the system 1. -2 0 2i and for the eigenvalue λ-2, the vector V-(1) is an eigenvector. we know that λ- (a) find the general solution; (b) determine if the origin is a spiral sink, a spiral source, or a center; (e) determine the direction of the oscillation in the phase plane (do the solutions go clockwise or countercdlocdkwise around the origin?); or counterclockwise (3 points) Given the system 1. -2 0 2i and for the eigenvalue...
The system of linear differential equations has the following solution e ( sitct)What is the type of the phase portrait for sin 4t + 3 cos 4t this system? O spiral source nodal source spiral sink center O nodal sink saddle
Problem 7. (1 point) a. Find the most genera reat valued solution to the inear system of diferential equations t' = [": -); x1 (1) = C C + C2 x2 (1) u b. In the phase plane, this system is best described as a source / unstable node sink / stable node O saddle center point / ellipses O spiral source spiral sink none of these
(1 point) 2. Find the most general real-valued solution to the linear system of diferential equations 7' = [4 4]z. x1 (1) -2iexp(-4t)exp(-21" 2i*exp(-4t)exp(21*t = C1 + C2 x2 (1) exp(-4t)exp(-21) exp(-4t)exp(2i*t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses O spiral source O spiral sink
Problem 7. (1 point) a. Find the most general real-valued solution to the linear system of differential equations X' = [ * ] x1(1) C1 x2(1) + C2 b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses O spiral source spiral sink none of these
8 -12 a. Find the most general real-valued solution to the linear system of differential equations zē' = [; . 9-13 x1(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 Ospiral sink none of these
4 -9 a. Find the most general real-valued solution to the linear system of differential equations a' = 31(t) . C1 + c2 22(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node O saddle O center point / ellipses spiral source O spiral sink O none of these
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) =
(1 point) a. Find the most general real-valued solution to the linear system of differential equations a' 2.(0) z(t) C + c b. In the phase plane, this system is best described as a O source / unstable node sink/stable node O saddle O center point/ ellipses spiral source Ospiral sink
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.