00:04
Now in this question, you asked you to solve the initial value problem, right? and of course, this x, we can rewrite it as, you know, this x1 and x2, right? i'm going to write like this, x1 and x2.
00:17
You have two components.
00:18
The initial value are given by this expression, right? and then how do we find the explanation of, how do we find the solution? well, first we need to assume that, you know, xt, so first we can assume that this x is kind of, is a risk of the form of this, right, is an exponential function basically, right? so we can actually assume of this form and find a gamma, right? so what we do is substitute this into this expression, and what do you get? you would get of his gamma, you will get a gamma minus the metrics, right? 3, 9, minus 1, minus 3, right? and you will find this gamma times a constant, a, you know, x, x, not.
01:06
Let me, let me read it, for example, as x, uh, right? so suppose the solutions of this firm, and then you have found this x not to be zero, right? and of course, from this, we see that the determinant of this matrix must be zero.
01:18
So in other words, the determinant of this, uh, three, uh, okay, is, um, three, we can write it as, you know, uh, the determinant of this is three, i can write a three minus gamma and the instance minus nine and this worm.
01:32
And this will be 3 plus gamma, right? i think that would be what we found, and we said the determinant of zero, right? we can find the variable gamma, right? so it's clear that, so is gamma, let's see what is correct...