Solution to Exercise: Fundamental Matrix for System of ODEs

[brad sue]

Hi, Please can someone help me on how to do this exercise.


Give a fundamental matrix for the system:
{x'(t)=-y(t)
{y'(t)=20x(t)-4y(t)

the solution is like:
{v1(t)=e^2t*cos(4t)[1;4]+e^2t*sin(4t)[-1;-2], v2(t)=e^2t*cos(4t)[1;4]+e^2t*sin(4t)[0;-4]}

[1;4]...are colunm vectors.
IT is just a form sample since it is a multiple choice question, I just took one solution to show you what it might look like.

Thank you,
B

 

[J77]

Assuming it's a standard type qu...

1. Write the system in matrix form.
2. Find the eigenvalues and eigenvectors.
3. Compare with the multiple choice of general forms you have.