Question

Find the general solution to the following linear system around the equilibrium point: x '1 =...

Find the general solution to the following linear system around the equilibrium point:

x '1 = 2x1 + x2

x '2 = −x1 + x2

(b) If the initial conditions are x1(0) = 1 and x2(0) = 1, find the exact solutions for x1 and x2.

(c) Plot the exact vector field (precise amplitude of the vector) for at least 4 points around the equilibrium, including the initial condition.

(d) Plot the solution curve starting from the initial condition x1(0) = 1 and x2(0) = 1 on the phase plane.

Homework Answers

Answer #1

Doubt in this then comment below.. i will help you..

.

please thumbs up for this solution..thanks .

.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the solution to the following system by converting the system to matrix form: x'1= 2x1+4x2,...
Find the solution to the following system by converting the system to matrix form: x'1= 2x1+4x2, x1(0)=0 x'2= x1-x2, x2(0)=-2
Find a particular solution to the given linear system of differential equations: dx1/dt = 4x1 +...
Find a particular solution to the given linear system of differential equations: dx1/dt = 4x1 + 5x2 dx2/dt = x1 + 8x2 , with initial conditions x1(0) = 6, and x2(0) = 0.
Linear Algebra find all the solutions of the linear system using Gaussian Elimination x1-x2+3x3+2x4=1 -x1+x2-2x3+x4=-2 2x1-2x2+7x3+7x4=1
Linear Algebra find all the solutions of the linear system using Gaussian Elimination x1-x2+3x3+2x4=1 -x1+x2-2x3+x4=-2 2x1-2x2+7x3+7x4=1
For parts a and b, find a basis for the solution set of the homogeneous linear...
For parts a and b, find a basis for the solution set of the homogeneous linear systems. Show all algebraic steps. a. x1 + x2 + x3 = 0. x1 - x2 - x3 = 0 b. x1 + 2x2 - 2x3 + x4 = 0. x1 - 2x2 + 2x3 + x4 = 0. for parts c and d use your solutions to parts a and b to find all solutions to the following linear systems. show all algebraic...
Transform the given system into a single equation of second-order x′1 =−8x1+9x2 x′2 =−9x1−8x2. Then find...
Transform the given system into a single equation of second-order x′1 =−8x1+9x2 x′2 =−9x1−8x2. Then find x1 and x2 that also satisfy the initial conditions x1(0) =7 x2(0) =3. Enter the exact answers. Enclose arguments of functions in parentheses. For example, sin(2x).
1.) either solve the given system of equations, or else show that there is no solution....
1.) either solve the given system of equations, or else show that there is no solution. x1 + 2x2 - x3 = 2 2x1 + x2 + x3 = 1 x1 - x2 + 2x3 = -1 2.) determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them. (a.) x(1) = (1, 1, 0) , x(2) = (0, 1, 1) , x(3) = (1, 0, 1)...
1)Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution,...
1)Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) x1 + 2x2 + 8x3 = 6 x1 + x2 + 4x3 = 3 (x1, x2, x3) = 2)Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express...
The matrix [−1320−69] has eigenvalues λ1=−1 and λ2=−3. Find eigenvectors corresponding to these eigenvalues. v⃗ 1=...
The matrix [−1320−69] has eigenvalues λ1=−1 and λ2=−3. Find eigenvectors corresponding to these eigenvalues. v⃗ 1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ and v⃗ 2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ Find the solution to the linear system of differential equations [x′1 x′2]=[−13 20−6 9][x1 x2] satisfying the initial conditions [x1(0)x2(0)]=[6−9]. x1(t)= ______ x2(t)= _____
Find the solution to the linear system of differential equations {x′ = 6x + 4y {y′=−2x...
Find the solution to the linear system of differential equations {x′ = 6x + 4y {y′=−2x satisfying the initial conditions x(0)=−5 and y(0)=−4. x(t) = _____ y(t) = _____
Find the solution to the linear system of differential equations: x'= -19x+30y y'= 10x+16y Satisfying the...
Find the solution to the linear system of differential equations: x'= -19x+30y y'= 10x+16y Satisfying the initial conditions: x(0)= -7 y(0)= -5
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT