00:01
Hello, welcome to this lesson.
00:03
In this lesson we would verify that the piecewise function y equals to negative x squared when x is less than zero and equals to x squared when x is greater than or equals to zero.
00:27
It's actually a solution for this differential equation.
00:32
What i'm going to do is i'm going to have the derivative of the piecewise function which would be negative 2x for x less than zero and this would be 2x for x greater than or equals to zero.
01:00
Alright, so let's see if the right side is equal to the left side.
01:06
Now, let's pick x times when x is less than zero.
01:15
So we have negative 2x plus 2y, the value of the y, this is negative x squared.
01:27
So negative x squared.
01:30
So this is equal to negative 2x squared plus 2x squared which is actually equals to zero.
01:43
Let's also look at the next part.
01:48
So actually let's pick up a value of x.
01:52
So the value of x equals to x is less than zero.
01:55
So let's pick negative one.
02:00
Negative one is less than zero.
02:02
So we have negative one minus two times negative one times minus two minus one.
02:13
So this is negative one times negative two which is positive two times negative one.
02:33
This is negative two.
02:36
Then actually this is one.
02:42
Okay and here we have negative one times negative two which is two, right, times negative one squared...