00:01
Hello, so we consider our given differential equation, and we compare it with the form mdx plus n -d -y is equal to zero.
00:10
So here we have that m is equal to x squared plus 2xy minus y squared, and n is going to be equal to y -squared plus 2xy minus x squared.
00:21
So we verify that equation here is not exact by comparing the terms the partial with respect to x of so n sub x and then m sub y.
00:33
So m sub y is going to be the partial derivative with respect to y of x squared plus 2x y minus y squared.
00:42
So that's going to give us, well, zero plus 2x minus 2 y.
00:46
Factoring a 2, we get 2 times x minus y.
00:50
And then taking n sub x is going to be the partial derivative of of n.
00:55
So the partial derivative to respect to x of y squared plus 2xy minus x squared.
01:00
That's going to be 0 plus 2y minus 2x.
01:03
That's going to be 2 times y minus x.
01:06
Then we see here that m sub y is not equal to n sub x.
01:10
So therefore the partial derivatives here are not equal.
01:13
So therefore we prove that the deference equation is not exact...