Lec 11 MIT 18.03 Differential Equations, Spring 2006
y prime and y double prime. So, q of x times y equal zero. The linearity of the equation, that is, the form in which it appears is going to be the key idea today. Today is going to be theoretical, but some of the ideas in it are the most important in the course. So, I don't have to apologize for the theory. Remember, the solution method was to find two independent y one, y two independent solutions. And now, I'll formally write out what independent means. There are different ways to say it. But for you, I think the simplest and most intelligible will be to say that y2 is not to be a constant multiple of y1. And, unfortunately, it's necessary to add, nor is y1 to be a constant multiple. I have to call it by different constants. So, let's call this one c prime of y2. Well, I mean, the most obvious question is, well, look. If this is not a constant times that, this can't be there because I would just use one over c if it was. Unfortunately, the reason I ...