Have I answered these questions on Laplace's equation correctly?

[lozzyjay]

Homework Statement

I missed the lecture on this so I just wanted to check if I am doing this correctly?

Which of the following functions obey Laplace’s equation?
a) Ψ(x, y) = 2xy
b) Ψ(x, y) = x^3 - 3y^2
c) Ψ(x, y) = x^4 - 6x^2.y^2
d) Ψ(x, y) = e^x.siny
e) Ψ(x, y) = sinxsinhy

Homework Equations

$$\nabla$$$$^{2}$$ = $$\partial^2/\partial x^2 + \partial^2/\partial y^2 + \partial^2/\partial z^2$$

The Attempt at a Solution

I am not showing me working out the partial derivatives of each question so I'm just showing the final line of my working.

a) 0 - 0 = 0 so yes

b) 6x - 6x = 0 so yes

c)12x^2 - 12y^2 - 12x^2 so no it doesn't

d) e^x.sin(y) - e^x.sin(y) = 0 so yes

e) -sin(x)sinh(y) + sin(x)sinh(y) = 0 so yes

 

[tiny-tim]

Hi lozzyjay!

ok except for:

b) 6x - 6x = 0 so yes

 

[lozzyjay]

Ah yes! Thank you! :)