\documentclass[11pt]{amsart}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   % ... or a4paper or a5paper or ... 
%\geometry{landscape}                % Activate for for rotated page geometry
%\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{epstopdf}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}

\title{Brief Article}
\author{The Author}
%\date{}                                           % Activate to display a given date or no date

\begin{document}
\maketitle
%\section{}
%\subsection{}

\begin{equation*}
u = \frac{N_v(x,y) \lambda \hat{u}(x,y) - N_v(x,y) I_t(x,y) I_x(x,y) - \hat{v}(x,y) I_x(x,y) I_y(x,y) + \hat{u}(x,y) I_y^2(x,y)}
{N_v(x,y)[N_v(x,y) \lambda + I_x^2(x,y) + I_y^2(x,y)]}
\end{equation*}

La solucion

\begin{equation*}
u = \hat{u}(x,y) - \frac{ (  I_x(x,y) \hat{u}(x,y) +  I_y(x,y) \hat{v}(x,y) + N_v(x,y) I_t(x,y) )I_x(x,y) }
{N_v(x,y)[N_v(x,y) \lambda + I_x^2(x,y) + I_y^2(x,y)]}
\end{equation*}


\begin{equation*}
v = \frac{N_v(x,y) \lambda \hat{v}(x,y) - N_v(x,y) I_t(x,y) I_y(x,y) - \hat{u}(x,y) I_x(x,y) I_y(x,y) + \hat{v}(x,y) I_x^2(x,y)}
{N_v(x,y)[N_v(x,y) \lambda + I_x^2(x,y) + I_y^2(x,y)]}
\end{equation*}

\end{document}  