Solving a systems of differential equations in terms of x(t) and y(t)

Intervenient

1. The problem statement, all variables and given/known data

x' ={{-1,1},{-4, 3}}*x, with x(0) = {{1},{1}}

Solve the differential equation where x = {{x(t)}, {y(t)}}

2. Relevant equations



3. The attempt at a solution

I have e^t*{{1},{-2}} + e^t*{{t},{2t+1}}

but I'm not sure how to get it in terms of what it's asking.





Edit: Please quick if you know how to do it. It's due at 4 AM :/ Crazy week on my end.

sunjin09

x'=Ax is solved by solutions of the form x(t)=x0e^{λt} where x0 is some initial vector, not the form you gave. You need to find out x0 and λ. I've seen this question quite a few times recently