- #1
Reshma
- 749
- 6
The Laplace's equations in 2-dimensions if V is the electric potential is given by:
[tex]\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0[/tex]
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?
[tex]\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0[/tex]
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?