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GILBERT STRANG: OK. Well my problem today is a little different. Because I dont have two initial conditions, as we normally have for a second-order differential equation. Instead, I have two boundary conditions. So let me show you the equation. So Im changing t to x because Im thinking of this as a problem in space rather than in time. So theres the second derivative. The minus sign is for convenience. This is the load. But heres the new thing. Im on an interval 0 to 1. And at 0-- let me take 0 for the two boundary conditions. So my solution somehow does something like this. Maybe up and back down. So its 0 there, 0 there, and in between it solves the differential equation. Not a big difference, but youll see that its an entirely new type of problem. OK. As far as the solution to the equation goes, there is nothing enormously new. I still have a y particular. A particular solution that solves the equation. And then I still have the y null, the homogeneous solution, any solutio