Finding a constant for a partial differential equation

In summary, the conversation was about finding the values of a constant, a, in a function u that satisfies a given partial differential equation. The suggestion was made to use polar coordinates as a possible substitution for the sum of x_i squared. One person also asked for help with removing an accidental "lightbulb" icon.
  • #1
KataKoniK
1,347
0
Can anyone help me with this question? I tried taking the derivative of u with respect to x and then summed the third derivative, but I'm getting nowhere. Any help would be great, thanks.

Let u(x1, x2, … , xn) = http://img480.imageshack.us/img480/1694/image0027hm.gif [Broken],[/URL] where a is a constant, and n is given.

Find all the values of the constant a, if any, for which the function u satisfies the partial differential equation http://img480.imageshack.us/img480/2918/image0044jl.gif [Broken] .
 
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  • #2
Do you think it's possible that you should be making a substitution for the sum of x_i squared? It just seems that polar coordinates might be an easier way to work the problem. Not that it would be easy.

Carl

Now. How do I make that little "lightbulb" that I accidentally clicked on go away?
 

1. What is a partial differential equation (PDE)?

A PDE is a mathematical equation that involves multiple variables and their partial derivatives. It is typically used to describe physical phenomena such as heat transfer, fluid flow, and electromagnetism.

2. Why is it important to find a constant for a PDE?

Finding a constant for a PDE is crucial in order to solve the equation and obtain a meaningful solution. The constant, also known as the arbitrary constant or the integration constant, is necessary to account for the variability in the PDE and helps to determine the specific solution for a given problem.

3. How do you find a constant for a PDE?

The constant for a PDE can be determined through the application of initial or boundary conditions. These conditions provide additional information about the system being modeled and narrow down the potential solutions for the PDE. By plugging in these conditions and solving for the constant, a specific solution for the PDE can be found.

4. Are there different types of constants for PDEs?

Yes, there are two types of constants that can be found for PDEs: particular constants and general constants. Particular constants are specific to a particular solution for a given set of initial or boundary conditions, while general constants are applicable to all solutions of the PDE and can be adjusted to fit different conditions.

5. Can a PDE have more than one constant?

Yes, a PDE can have multiple constants depending on the complexity of the equation and the number of conditions provided. In some cases, a PDE may require multiple constants in order to obtain a unique solution. However, the number of constants needed is typically determined by the order and type of the PDE.

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