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2 - 5 For each system below, (a) solve the initial value problem, and (b) determine...
There are ten problems totaling 10 points. Show all your work! 1-4 For each system below, (a) sol...
just problem number 4 please!
thank you!
There are ten problems totaling 10 points. Show all your work! 1-4 For each system below, (a) solve the initial v stability of the critical point at (0,0) 1. alue problem, and (b) determine the type and x' =-4x1 + 5x2 X2,--5x1 + 4x2 x1(0) -16, x2(0) 25. x'= 6x1 + x2 x1(0) 6, X2(0) = 4 2. xi(12345e) 55, X2(12345e)--729 3 xi-43x Xi(-101) = 9, x2(-101) 5 4 x' = 2x1-x2 x2,=...
3 Linear systems 18. Solve the linear system of equations using the Naive Gauss elimination metho...
3 Linear systems 18. Solve the linear system of equations using the Naive Gauss elimination method x,+x: + x) = 1 +2x, +4x1 x 19. Solve the linear system of equations using the Gauss elimination method with partial pivoting 12x1 +10x2-7x3=15 6x, + 5x2 + 3x3 =14 24x,-x2 + 5x, = 28 20. Find the LU decomposition for the following system of linear equations 6x, +2x, +2, 2 21. Find an approximate solution for the following linear system of equations...
7. Find and classify the type and stability of the critical point for each system below...
7. Find and classify the type and stability of the critical point for each system below x' =-2x1-3x2 + 8 xz'= 3x1 + 2x2-8 Where α is a real number.
USE THE BRANCH AND BOUND (B&B) ALGORITHM!!!! Please show all the steps, including the branchi...
USE THE BRANCH AND BOUND (B&B) ALGORITHM!!!!
Please show all the steps, including the branching and the
graphs.
362 Chapter 9 nteger Linear Programming 9-56. Develop the B&B tree for each of the following problems. For coaseni xi as the branching variable at node 0. (a) Maximizez 3xi + 2r2 subject to x, x2 2 0 and integer (b) Maximizez2r, + 3x2 subject to 5x 7x2 s 35 x1, x2 0 and integer (c) Maximizezx + x2 subject to 2x1...
Solve the given initial value problem. | | - = 4x + y; | (0) =...
Solve the given initial value problem. | | - = 4x + y; | (0) = 3 2 = -2x+y, y(0)=0 | The solution is x(t) = I and y(t) = D. Find the critical point set for the given system. | = y +5 = x + y - 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The set of critical points is { }. (Use a...
3. (5 pts each) For each system, write the initial augmented matrix for the system. DO...
3. (5 pts each) For each system, write the initial augmented matrix for the system. DO NOT SOLVE. X1- 2x3 9 4x, +3x2 + 2x,=-11 -4x2+x3 19 lo le orle u (3x, +5x2-2x, + x4-2x, = 0 4x1-3x2+ 2x3+x 21 b. -4x2+x4-xs = 9 4. (5 points each) State the solutions from each reduced matrix (if they exist) [1 0 1 0 lo o 1 0 01 5 [1 0 0111 b. 0 1 0 3 lo o ol5 a...
Solve the initial value problem. d²y = 5 - 7x, y' (O) = 8, y(0) =...
Solve the initial value problem. d²y = 5 - 7x, y' (O) = 8, y(0) = 2 dx² 5 7 2 ОА. y= 2 + 3 X° - 8x-2 OB. y= 2 OC. y - x2 +8x + 2 OD. y=5x² + 7x3 + 8x + 2
Solve the initial value problem with x'(t) = A, for t20 with x(0)= Classify the nature...
Solve the initial value problem with x'(t) = A, for t20 with x(0)= Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction and/or repulsion. -2 -4 A= 10 -16 127 a. X(t)= is a saddle point b. X(t)= 121 + 6 (0,0) is an attractor 1 --[1]26. (0,0) --[] $]e=121+6[71]e-, (0,0) is an attractor d. x(e) = - [] -e[1]26. (0,0) is repeller e....
5.3.1 Convert the given initial value problem into an initial value problem for a system in...
5.3.1 Convert the given initial value problem into an initial value problem for a system in normal form. y"(t) - 4y'(t) + 58+ y(t) = 7t y(0) = 3, y'(0) = - 3 Let xy = y and X2 = y'. Complete the differential equation and initial condition for X (Type an expression using t, xy, and X2 as the variables.) x'= X (0)=
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the syst...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
just problem number 4 please!
thank you!
There are ten problems totaling 10 points. Show all your work! 1-4 For each system below, (a) solve the initial v stability of the critical point at (0,0) 1. alue problem, and (b) determine the type and x' =-4x1 + 5x2 X2,--5x1 + 4x2 x1(0) -16, x2(0) 25. x'= 6x1 + x2 x1(0) 6, X2(0) = 4 2. xi(12345e) 55, X2(12345e)--729 3 xi-43x Xi(-101) = 9, x2(-101) 5 4 x' = 2x1-x2 x2,=...
3 Linear systems 18. Solve the linear system of equations using the Naive Gauss elimination method x,+x: + x) = 1 +2x, +4x1 x 19. Solve the linear system of equations using the Gauss elimination method with partial pivoting 12x1 +10x2-7x3=15 6x, + 5x2 + 3x3 =14 24x,-x2 + 5x, = 28 20. Find the LU decomposition for the following system of linear equations 6x, +2x, +2, 2 21. Find an approximate solution for the following linear system of equations...
7. Find and classify the type and stability of the critical point for each system below x' =-2x1-3x2 + 8 xz'= 3x1 + 2x2-8 Where α is a real number.
USE THE BRANCH AND BOUND (B&B) ALGORITHM!!!!
Please show all the steps, including the branching and the
graphs.
362 Chapter 9 nteger Linear Programming 9-56. Develop the B&B tree for each of the following problems. For coaseni xi as the branching variable at node 0. (a) Maximizez 3xi + 2r2 subject to x, x2 2 0 and integer (b) Maximizez2r, + 3x2 subject to 5x 7x2 s 35 x1, x2 0 and integer (c) Maximizezx + x2 subject to 2x1...
Solve the given initial value problem. | | - = 4x + y; | (0) = 3 2 = -2x+y, y(0)=0 | The solution is x(t) = I and y(t) = D. Find the critical point set for the given system. | = y +5 = x + y - 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The set of critical points is { }. (Use a...
3. (5 pts each) For each system, write the initial augmented matrix for the system. DO NOT SOLVE. X1- 2x3 9 4x, +3x2 + 2x,=-11 -4x2+x3 19 lo le orle u (3x, +5x2-2x, + x4-2x, = 0 4x1-3x2+ 2x3+x 21 b. -4x2+x4-xs = 9 4. (5 points each) State the solutions from each reduced matrix (if they exist) [1 0 1 0 lo o 1 0 01 5 [1 0 0111 b. 0 1 0 3 lo o ol5 a...
Solve the initial value problem. d²y = 5 - 7x, y' (O) = 8, y(0) = 2 dx² 5 7 2 ОА. y= 2 + 3 X° - 8x-2 OB. y= 2 OC. y - x2 +8x + 2 OD. y=5x² + 7x3 + 8x + 2
Solve the initial value problem with x'(t) = A, for t20 with x(0)= Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction and/or repulsion. -2 -4 A= 10 -16 127 a. X(t)= is a saddle point b. X(t)= 121 + 6 (0,0) is an attractor 1 --[1]26. (0,0) --[] $]e=121+6[71]e-, (0,0) is an attractor d. x(e) = - [] -e[1]26. (0,0) is repeller e....
5.3.1 Convert the given initial value problem into an initial value problem for a system in normal form. y"(t) - 4y'(t) + 58+ y(t) = 7t y(0) = 3, y'(0) = - 3 Let xy = y and X2 = y'. Complete the differential equation and initial condition for X (Type an expression using t, xy, and X2 as the variables.) x'= X (0)=
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
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