# Solution to Laplaces equation

1. Oct 28, 2005

### Reshma

The Laplace's equations in 2-dimensions if V is the electric potential is given by:
$$\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0$$
Since this is a second order partial differential equation, the simple rules of an ordinary differential do not apply. The solution will not contain a definite number of arbitrary constants. So how is a general solution obtained for this equation?

2. Oct 28, 2005

3. Nov 1, 2005

### starfield

see Introduction to Electrodynamics by David J Griiffiths....
there is a very good introiduction to Partial differential equations in it....

4. Nov 1, 2005

### ZapperZ

Staff Emeritus
Or see Mary Boas "Mathematical Methods in the Physical Science". Chances are, if you're having problems with this, you may need to look at a bunch of other mathematical techniques in 2nd order partial differential equation and how they are used in physics. This book covers such a thing.

Zz.

5. Nov 2, 2005

### dextercioby

1.Bring it to canonical form.
2.Identify the type of problem you're dealing with depending on the initial/boundary conditions.
3.Using the separation of variables is the easiest way to get a particular solution.

Daniel.