Lec 26 MIT 18.03 Differential Equations, Spring 2006
I just want to remind you of the main facts. The first thing that you have to do is, of course, we are going to have to be doing it several times today. That is the system we are trying to solve. And the first thing you have to do is find a characteristic equation which is general form, although this is not the form you should use for two-by-two, is A minus lambda I equals zero. And its roots are the eigenvalues. And then with each eigenvalue you then have to calculate its eigenvector, which you do by solving the system (A minus lambda1, let's say, times I) alpha equals zero because the solution is the eigenvector alpha 1. And then the final solution that you make out of the two of them looks like alpha 1 times e to the lambda 1t. Of course you do that for each eigenvalue. You get the associated eigenvector. And then the general solution is made up out of a linear combination of these individual guys with constant coefficients. The lecture today is devoted to the two ...