# Notation for separable partial differential equations

1. Dec 6, 2010

### frozenguy

Hey.. I ran across some problems and the notation used is a little different from what I've seen before.

considering U(x,y)=X(x)Y(y)
Sometimes I'll see Uxx for $$\frac{d^{2}u}{dt^{2}}$$ which equals X''Y
Or Ux for $$\frac{du}{dt}$$ which equals X'Y

Is that a redundant way of saying the partial derivative of U with respect to x?

Or is it saying the derivative of the partial derivative of U with respect to x?

As I originally read it, I considered it X'Y, but now I'm wondering if maybe its X"Y.

Thanks!

2. Dec 7, 2010

### AlephZero

I think you meant
Uxx for $$\frac{\partial^{2}u}{\partial x^{2}}$$
or
Ux for $$\frac{\partial u}{\partial x}$$

Out of context, I would take that to mean $$\frac{d}{dt} \left(\frac{\partial u}{\partial x}\right)$$, but the context might indicate it meant something different. (The difference between $$d$$ and $$\partial$$ is not a typo.)

Last edited: Dec 7, 2010
3. Dec 7, 2010

### frozenguy

For example: $$U^{'}_{x}=U^{'}_{y}+U$$