Question

the solution of Laplace equation in two dimensions.​

Answer 1

The solution of Laplace's equation in one dimension gives a linear potential, has the solution , where m and c are constants. The solution is featureless because it is a monotonically increasing or a decreasing function of x.

Answer 2

Answer:

$\frac{\partial^{2} u}{dx^{2} } +\frac{\partial^{2}u}{\partial y^{2} } =0$ is the solution of Laplace equation in two dimensions.

Step-by-step explanation:

Explanation:

In two and three dimensions , Laplace's equation says that at each

point ,the sum of the concavities is zero .

$\frac{\partial^{2} u}{dx^{2} } +\frac{\partial^{2}u}{\partial y^{2} } =0$ ...........(i)

This equation represents a linear , quadratic partial differential equation.

In this equation the dependent variable u(x ,y) is the function of its arguments

and it depends on the independent variable  x and y in order  

to find numerical solution to the laplace equation.

There is no general solution .

Final answer:

Hence  the solution of Laplace equation in two dimensions is

$\frac{\partial^{2} u}{dx^{2} } +\frac{\partial^{2}u}{\partial y^{2} } =0$ .