\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{notadoctor}
\pdfinfo{
  /Title (diffeq.pdf)
  /Creator (Cheatography)
  /Author (notadoctor)
  /Subject (DiffEq Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{A3A3A3}
\definecolor{LightBackground}{HTML}{F3F3F3}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{DiffEq Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{notadoctor} via \textcolor{DarkBackground}{\uline{cheatography.com/43403/cs/12924/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}notadoctor \\
  \uline{cheatography.com/notadoctor} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 25th September, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{3.1 Modeling with Linear DE}}  \tn
% Row 0
\SetRowColor{LightBackground}
Radioactive Decay & x(t)=x\_0*e\textasciicircum{}(kt) \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Population & P(t) = P\_0*e\textasciicircum{}(kt) \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Compound Interest & S(t)=S\_0*e\textasciicircum{}(rt) \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
Cooling/Heating & T(t)=T\_m+(T\_0-T\_m)*e\textasciicircum{}(kt) \tn 
% Row Count 5 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Mixing of Two Fluids & dA/dt=R\_in-R\_out \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Examples}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Population increases proportional to \#people at time t. If initial population P0 has doubled in 7 years, how long will it take to triple/quadruple? \newline % Row Count 3 (+ 3)
2P0/P0=e\textasciicircum{}(kt) =\textgreater{} ln(2)=kt =\textgreater{} k=ln(2)/7 =\textgreater{} (ln(2)/7) \newline % Row Count 5 (+ 2)
t(trip)=ln(3)/{[}ln(2)/7{]} = 11.09yr =\textgreater{} t(quad)=ln(4)/{[}ln(2)/7{]} = 14yr \newline % Row Count 7 (+ 2)
A tank contains 1000 L pure h2o. Brine w/ 1 kg/L salt pumped in @ 6L/min; the well-mixed solution is pumped out at the same rate. When will concentration = 0.5kg/L \newline % Row Count 11 (+ 4)
A'(t)=Rin-Rout =\textgreater{} Rin=6kg/min; \seqsplit{Rout=(A/1000kg/L)*(6L/min)=3A/500} kg/min \newline % Row Count 13 (+ 2)
A'(t)+3A/500=6 =\textgreater{} A(t)=1000+Ce\textasciicircum{}(-3t/500) =\textgreater{} A(0)=0 =\textgreater{} C=-1000 \newline % Row Count 15 (+ 2)
1000=1000e\textasciicircum{}(-3t/500)=500 =\textgreater{} e\textasciicircum{}(-3t/500)=1/2 =\textgreater{} t=115.53s% Row Count 17 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}