sor the following system, (a) provide the general solution, (b) 3: a tive properties of the...
5: For the following system, (a) provide the general solution, (b) provide a sketch showing the qualitative properties of the system, (c) specify what type ((spiral) source/sink, center, saddle) of equilibrium point the origin is. You should include any straight-line solutions as well as indicate more general types of solution curves. Be sure to indicate the direction of motion along any solution curve dY (1 -1 5: For the following system, (a) provide the general solution, (b) provide a sketch...
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...
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
3 - 36 a. Find the most general real-valued solution to the linear system of differential equations = 2. 1 -3 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 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
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
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
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
a. Find the most general real-valued solution to the linear system of differential equations a' 2 -9 -2 2. 21(t) 음을 + C2 22(t) b. In the phase plane, this system is best described as a O source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these preview ang