Solving LaPlace Equation: Water Potential=-KH=-x^3y+xy^3+5

[maureen101]

Homework Statement

water potential=-KH=-x^3y+xy^3+5. Is this a solution to the Laplace equation and is yes, show how

Homework Equations

LaPlace equation= Partial derivative^2 of H/partial deriv x^2+partial deriv^2H/partial deriv y^2=0

The Attempt at a Solution

I have absolutely no idea. Somebody please help me!

 

[Dick]

You don't know how to find partial derivatives??

 

[maureen101]

This is for a soil physics class that did not have any prerequisites but we are doing differential equations and I stopped my math education way before calculus. (I did my undergrad over 20 years ago). The teacher has shown some partial derivative equations but this x^3y+xy^3 +5 equation just looks algebraic to me. I can't relate it at all to the LaPlace equation. I'm on day 4 of trying to figure this out and the teacher won't give any help.

 

[HallsofIvy]

If you are in a class where you are expected to find partial derivatives and you have never taken Calculus, then you clearly do not have the prerequisites for the course and probably should drop it as soon as possible.

 

[Dick]

So you don't know how to find derivatives either? That's a little awkward. You really have to know how to do that before you can say much about the Laplace equation. Do you know what a derivative is?

 

[maureen101]

Nobody in the class knows how to do derivitives and only two have had calculus. The teacher has strange expectations since he asks questions about things he has neither taught nor expressed in advance that they must have already been learned. And the semester ends in a a few weeks, so dropping is a little silly. Back to getting actual help...
I do know what a partial derivative is. Do I need to start with the x,y equation and do a pertial derivative on each component (i.e x^3y and xy^3) or do I start with the LaPlace equation and try to come up with the x,y equation.

 

[tylerc1991]

You have the equation itself, now all you have to do is take a second partial derivative with respect to x, then a second partial derivative with respect to y, add them, and verify that you get 0.

 

[Dick]

Nobody in the class knows how to do derivitives and only two have had calculus. The teacher has strange expectations since he asks questions about things he has neither taught nor expressed in advance that they must have already been learned. And the semester ends in a a few weeks, so dropping is a little silly. Back to getting actual help...
I do know what a partial derivative is. Do I need to start with the x,y equation and do a pertial derivative on each component (i.e x^3y and xy^3) or do I start with the LaPlace equation and try to come up with the x,y equation.

Ok, so maybe you can bluff this one out. Take just the part x^3y. What's the first partial derivative with respect to x? Second derivative?

 

[maureen101]

Is the answer to the first derivative of x^3y=3x^2y

 

[tylerc1991]

Is the answer to the first derivative of x^3y=3x^2y

that is one of the partial derivatives, yes.

 

[Dick]

Is the answer to the first derivative of x^3y=3x^2y

That's the first derivative with respect to x. What's second with respect to x? Then you have to do the y derivatives. Then you have to do the same thing with the xy^3 part. Then don't forget there is minus sign in front of the first one. It's really not that hard if you got that first x derivative. Just more of the same.