Let us have those functions it affects why is execute minus five X. Y square. We want to check if this function is a solution to the to this partial differential equation. Okay, so X times to cross partial derivatives minus uh minus, particularly with respect to why it's a good 20 So we're just gonna put this function in this form and see if is going to give you zero after the this operation. So you're gonna take it at first partial derivative with respect to X.
So this is gonna be three X square. But this time you should be able to do partial derivatives, right? Otherwise you can watch the previous tutorials to see how we do it. So this is just gonna be straightforward uh five Y squared. And then I'm gonna do F X. Y.
This is fx. So just to get partial derivative with respect to Y. And you're just gonna get negative 10. Why? Because this is a constant. Uh What is F.
Y. Well that is negative 10, right? X. Y. As well? This is supposed to be why? Okay, so now we're gonna put it in this form, So x. Now this one, is that okay? So that is going to be negative 10 Y.
So in fact gonna put it this way it's gonna be negative 10 X. Y. Right? Because this is X. And this one is this one so it gives you that then uh minus. Now this is F.
Y, F. Y. Is this guy? So I'm just gonna put it in place of it. Yeah. Now what does that give you? Well, this thing is negative 10 X Y minus negative, negative is positive is gonna plus, right, 10 X.
Y. So negative 10 X Y plus 10 X. Y. Is going to give you zero. So you can see that uh this guy is giving you zero.
So it means that it satisfies this equation, right? Because this one is zero and this one is zero. So the portrait differential equation is satisfied.