Need help with partial differential equation

In summary, the conversation discusses how to show that two sides of an equation are equal, with the equation being ∂2z/∂x∂y = ∂2z/∂y∂x. The conversation includes a discussion on taking partial derivatives and clarifying the meaning of relevant equations. The final step is finding ∂z/∂x and ∂z/∂y to complete the proof.
  • #1
Needhelp2013
10
0

Homework Statement


Given that z = √3x/y show that:


Homework Equations


2z/∂x∂y = ∂2z/∂y∂x

The Attempt at a Solution

 
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  • #2
Both sides of that equation are the same, did you mistype something?
 
  • #3
Yes I did, that's it sorted now.
 
  • #4
Ahh, as I suspected. Have you made an attempt yet?
 
  • #5
Thanks for spotting that.No I am pretty lost to be honest. I am fairly new to this. I believe I am working with the Laplace equation though
 
  • #6
Needhelp2013 said:
Thanks for spotting that.No I am pretty lost to be honest. I am fairly new to this. I believe I am working with the Laplace equation though

I think you're thinking too hard, you know how to take a partial derivative I assume?
 
  • #7
The equation under "Relevant Equations" is what you're trying to show, correct?
 
  • #8
Yes the equation under "Relevant Equations" is what I'm trying to show. There could be a simple solution but I'm missing it. I tried substituting what 'z=' into the laplace equation but that didnt get me anywhere.
 
  • #9
Needhelp2013 said:
I tried substituting what 'z=' into the laplace equation but that didnt get me anywhere.

Exactly what I meant by thinking too hard. All that it's asking you to do is show that if you take the derivative of z with respect to x and then y, it's the same as taking the derivative of z with respect to y and then x. In other words, show:

[itex]\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y}) [/itex]

Does that make any more sense now?
 
  • #10
I am just trying to work out how to read the latex way of writing equations. Ill get it. Thanks for that.
 
  • #11
bossman27 said:
Exactly what I meant by thinking too hard. All that it's asking you to do is show that if you take the derivative of z with respect to x and then y, it's the same as taking the derivative of z with respect to y and then x. In other words, show:

[itex]\frac{\partial}{\partial y}(\frac{\partial z}{\partial x}) = \frac{\partial}{\partial x}(\frac{\partial z}{\partial y}) [/itex]

Does that make any more sense now?

Is your equation meaning this ∂y/zx = ∂x/zy

any other help would be great becuase I am struggling to realize where to go next.
 
  • #12
You can't read that equation? It should read: ∂/∂y(∂z/∂x) = ∂/∂x(∂z/y)
 
  • #13
bossman27 said:
You can't read that equation? It should read: ∂/∂y(∂z/∂x) = ∂/∂x(∂z/y)

Thanks again.Is the next step now to bring the ∂z over to the other side and that is it complete?
 
  • #14
No, figure out the parts in the parentheses first. That is, find ∂z/∂x and ∂z/∂y.

You don't seem to be familiar with taking partial derivatives, so here's a quick explanation:

∂z/∂x = the derivative of z with respect to x; treat y as if it were a constant (i.e. just a number). Simply take the x derivative like you would for dz/dx, if y was just some number.

∂z/∂y is exactly the same, just switch x and y in my instructions.
 

1. What is a partial differential equation?

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables and their partial derivatives. It is used to describe how a system changes over time and space.

2. Why do we need help with solving partial differential equations?

Partial differential equations can be complex and difficult to solve, making them challenging for scientists and mathematicians. Seeking help from others can offer new perspectives and approaches to solving these equations.

3. What are some common techniques for solving partial differential equations?

Some common techniques for solving partial differential equations include separation of variables, Fourier transforms, and numerical methods such as finite differences and finite elements.

4. How are partial differential equations used in science?

Partial differential equations are used in many areas of science, such as physics, engineering, and biology. They can be used to model and understand complex systems and phenomena, making them a powerful tool for scientific research.

5. Can partial differential equations be solved analytically?

In some cases, partial differential equations can be solved analytically, meaning a closed-form solution can be found. However, for more complex equations, numerical methods are often used to approximate the solution.

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