Lec 24 MIT 18.03 Differential Equations, Spring 2006
For the rest of the term, we are going to be studying not just one differential equation at a time, but rather what are called systems of differential equations. Those are like systems of linear equations. They have to be solved simultaneously, in other words, not just one at a time. So, how does a system look when you write it down? Well, since we are going to be talking about systems of ordinary differential equations, there still will be only one independent variable, but there will be several dependent variables. I am going to call, let's say two. The dependent variables are going to be, I will call them x and y, and then the first order system, something involving just first derivatives, will look like this. On the left-hand side will be x prime, in other words. On the right-hand side will be the dependent variables and then also the independent variables. I will indicate that, I will separate it all from the others by putting a semicolon there. And the same way...