Writing partial differential equation like u_t=u_xx

Question

I have a problem writing the heat equation in latex. I would like to write it by starting with \begin{equation} and ending with \end{equation}. I tried doing the following:

\begin{equation}
\{$u_t(x,t)=u_{xx}(x,t)$} wherex $\epsilon$ ${\rm I\!R}$\  and $t>0$  
\end{equation}

The answer I got was this:

LaTeX Warning: You have requested package `',
               but the package provides `esdiff'.

and

! Display math should end with $$.
<to be read again> 
                   u
l.51 \{$u
         _t(x,t)=u_{xx}(x,t)$$} where x $\epsilon$ ${\rm I\!R}$\  and $t>0$
? 

Does anyone know how to write the heat equation in latex and have the text on the same line? David

Answer 1

Are you maybe looking for the following?

\documentclass{article}
\usepackage{amsmath}  % for \text macro
\usepackage{amssymb}  % for \mathbb macro
\begin{document}
\begin{equation}
\{ u_t(x,t)=u_{xx}(x,t)\}, \text{ where $\epsilon\in\mathbb{R}$ and $t>0$}
\end{equation}
\end{document}

Alternatively, might you be looking for the following?

\documentclass{article}
\usepackage{amsmath}  % for \text macro
\usepackage{amssymb}  % for \mathbb macro
\begin{document}
\begin{equation}
u_t(x,t)=u_{xx}(x,t), \text{ where $x\in\mathbb{R}$ and $t>0$}
\end{equation}
\end{document}

Answer 2

Please always provide complete small documents that reproduce the error, not just fragments.

equation puts you in math mode so you should not use $ to re-start math mode inside that.

Do not use \rm in latex (it is just for compatibility with the previous version, LaTeX2.09, which has not been released since 1992)

Don't use I\!R for a double struck R use \mathbb{R} don't use \epsilon for set membership.

\begin{equation}
u_t(x,t)=u_{xx}(x,t) \text{ where } x \in \mathbb{R} \text{ and }  t>0  
\end{equation}

The package error I would guess you did

\input{esdiff.sty}

instead of

\usepackage{esdiff}

Answer 3

Don't know if I got the equations right (your text was a bit confusing) but here is a working (and slightly corrected in terms of coding) version

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}

\begin{equation}
u_{t}\left(x,t\right)=u_{xx}\left(x,t\right) \text{where}~\epsilon = \mathrm{I!R}~\text{and}~t>0
\end{equation}

\end{document}