00:01
All right, so for this problem, let's go ahead and start off by identifying whether it's an exact differential equation or not.
00:07
So the way we do that was we take the partial to the left -hand side and the right -hand side.
00:12
And if they equal one another, we can conclude that as exact.
00:15
So we'll have partial y of sine y minus y -sign x, and we'll have partial x of cosine x plus x cosine y minus y.
00:33
Left -hand side when we take the partial derivative with respect to y, we get cosine y minus, let's see, sine x.
00:45
On the right -hand side, we get, let's see, this goes to negative sine x plus cosine y plus zero, or we can completely ignore it.
01:04
And these do, in fact, equal another.
01:06
So we can conclude that it is an exact differential equation that we have...