00:01
Here we have a second order differential equation, and they want us to find a general solution for that.
00:08
So we can identify b is a coefficient of the first derivative term, and that's minus 3, and c is the coefficient of the zero derivative term, or the, you know, just the y term, and that's 2.
00:24
Then we can calculate b squared minus 4c, and that turns out to be 1, which is greater than 0 .0 .0 .0 .0.
00:30
So writing this as an exponential, an exponential form will be the most convenient form to write it.
00:39
All the forms that they give at the book are actually mathematically equivalent as long as you, as long as you are happy to deal with complex numbers.
00:48
They're all mathematically equivalent, but you have to, you just need complex numbers to make them.
00:55
So we can just say, you know, use the characteristic equation is one, is 1, you know, is r squared minus 3r plus 2 equals 0, right? and so we can find the roots of that...