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How can I do this without the cases?

$\begin{cases} 
 \dfrac{\partial u(x,y)}{\partial x}=2x=\dfrac{\partial v(x,y)}{\partial y} \\ 
 \dfrac{\partial u(x,y)}{\partial y}=-2y=- \dfrac{\partial v(x,y)}{\partial x} 
 \end{cases} 
 \forall (x,y)\in \mathbb{R}^2$
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2  
aligned instead of cases? With a & to start the rows. Welcome to TeX.sx! –  egreg Feb 28 '13 at 16:02
    
For your information, if you type 4 spaces before a line, it will be shown as code. –  Ignasi Feb 28 '13 at 16:03
    
do you wanna avoid the brace or just do it in another way with brace? –  Rico Feb 28 '13 at 16:09
    
wanna avoid the brace –  Henfe Feb 28 '13 at 16:12

3 Answers 3

up vote 6 down vote accepted

Looking at the typeset result, I'd say you're looking not for cases or aligned, but alignedat (or its standalone version, alignat).

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}

\noindent Standalone:
\begin{alignat*}{99}
    \dfrac{\partial u(x,y)}{\partial x}&{}={}& 2&x={}&  &\dfrac{\partial v(x,y)}{\partial y} \\ 
    \dfrac{\partial u(x,y)}{\partial y}&{}={}&-2&y={}& -&\dfrac{\partial v(x,y)}{\partial x} 
\end{alignat*}
Embedded:
\begin{align*}
  \begin{alignedat}{99}
    \dfrac{\partial u(x,y)}{\partial x}&{}={}& 2&x={}&  &\dfrac{\partial v(x,y)}{\partial y} \\ 
    \dfrac{\partial u(x,y)}{\partial y}&{}={}&-2&y={}& -&\dfrac{\partial v(x,y)}{\partial x} 
  \end{alignedat}
  &&
  \forall x \in \mathbb{R}
\end{align*}

\end{document}

The {99} argument is there to satisfy an obtuse requirement of the environment: it specifies the maximum number of columns. I generally don't care to count, so I just make it absurdly large.

enter image description here

It's also possible to have the 2x centered, as tohecz requests, but this entails a small amount of hackery.

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}

\noindent Default
\begin{align*}
  \begin{alignedat}{99}
    \dfrac{\partial u(x,y)}{\partial x}&{}={}& 2&x={}&  &\dfrac{\partial v(x,y)}{\partial y} \\ 
    \dfrac{\partial u(x,y)}{\partial y}&{}={}&-2&y={}& -&\dfrac{\partial v(x,y)}{\partial x} 
  \end{alignedat}
  &&
  \forall x \in \mathbb{R}
\end{align*}
$2x$ centered:
\begin{align*}
  \begin{alignedat}{99}
    \dfrac{\partial u(x,y)}{\partial x}&{}={}&\omit\hfil$2x$\hfil&{}={}&  &\dfrac{\partial v(x,y)}{\partial y} \\ 
    \dfrac{\partial u(x,y)}{\partial y}&{}={}& -2y &{}={}& -&\dfrac{\partial v(x,y)}{\partial x} 
  \end{alignedat}
  &&
  \forall x \in \mathbb{R}
\end{align*}
\end{document}

Namely, you have to remove the "template" from the column containing 2x and replace it with the necessary glue (not forgetting the $ $, because those are normally included in the template). This entails a slightly different arrangement of columns than before, since now we want to keep the entire monomial together.

enter image description here

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The extra space in fron of 2x seems to be disturbing to me. If you really want all the = aligned, you might consider centering 2x there ;) –  yo' Feb 28 '13 at 16:58
    
@tohecz: I like to have the variables aligned, but that could just be my linear algebra lectures talking. –  Ryan Reich Feb 28 '13 at 16:59
    
I don't like it because it looks like that a - is missing in the first line :-/ –  yo' Feb 28 '13 at 17:01
    
@tohecz: How do you like my new example? –  Ryan Reich Feb 28 '13 at 17:13
    
+1, just there's still the same problem in front of dv/dy ;) –  yo' Feb 28 '13 at 17:15

amsmath provides a bunch of environments for alignments; in this case you're probably looking for aligned:

\documentclass{article}
\usepackage{amsmath,amssymb}

\begin{document}

\[
\begin{aligned} 
& \dfrac{\partial u(x,y)}{\partial x}=2x=\dfrac{\partial v(x,y)}{\partial y} \\ 
& \dfrac{\partial u(x,y)}{\partial y}=-2y=- \dfrac{\partial v(x,y)}{\partial x} 
\end{aligned}
\quad
\forall (x,y)\in \mathbb{R}^2
\]
\end{document}

enter image description here

I'd never use it inline, though.

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Don't forget \! before aligned. –  stalking is prohibited Oct 29 '13 at 5:47

Do you mean literally not using "cases" as in this?

$
   \begin{array}{l}
     \dfrac{\partial u(x,y)}{\partial x}=2x=\dfrac{\partial v(x,y)}{\partial y} \\ 
     \dfrac{\partial u(x,y)}{\partial y}=-2y=- \dfrac{\partial v(x,y)}{\partial x} 
   \end{array}
   \forall (x,y)\in \mathbb{R}^2
$

Or am I not understanding the question? [I edited to remove the brace]

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