Need help with Laplace's Equation

  • Thread starter tesla93
  • Start date
  • #1
23
0

Homework Statement



Determine whether each of the following functions is a solution of Laplace’s
equation uxx + uyy = 0.

x^3 + 3xy^2

ux=3x^2

uxx=6x

uy=6xy^2

uyy=6x

6x+6x=12x and is therefore not a solution

Did I do that right? I'm just learning about this topic and it's a little hard to understand. Can anyone give any advice as to if I approached this correctly?

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
179
4
while your result is correct, your steps are not written down correctly.
 
  • #3
833
30
Your derivatives are wrong. The procedure is correct, but your partial derivatives are wrong.

You have: [tex]f(x,y)=x^3+3xy^2[/tex]
Then, the derivative with respect to x is:
[tex]f_x(x,y)=3x^2+3y^2[/tex]

Everything else is okey. The result you found is fine because when you take the second derivative with respect to x the term involving y vanishes.
 

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