Text Formatting ⇒ managing long equation

[teddy0625]

I have this one very long equation which can not be displayed on one page as it can be seen from the attachment. I want to know how I can display it properly.
Thanks!

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Code, edit and compile here:

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\documentclass[a4paper,12pt,twoside]{book}
\usepackage{amsmath,amssymb,amsfonts,geometry} % Typical maths resource packages
\usepackage{xcolor}                    % For creating coloured text and background
\usepackage{hyperref}                 % For creating hyperlinks in cross references
\usepackage{graphicx}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{teo}{Theorem}[section]
\usepackage{fancyhdr}
\pagestyle{fancy}
  \renewcommand{\chaptermark}[1]{\markboth{\MakeUppercase{\chaptername \ \thechapter \ \ #1}}{}}
  \fancyhf{}%clear all header and footer fields
    \fancyhead[LO]{\nouppercase{\rightmark}}
    \fancyhead[RE]{\nouppercase{\leftmark}}
       \fancyhead[RO,LE]{\thepage}
\def\chem#1#2{ {{\scriptscriptstyle#1\atop\longrightarrow}\atop{\longleftarrow\atop \scriptscriptstyle#2}} }
\begin{document}
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\subsection{Linearization stability parallel flow (Rayleigh equation)}
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Now, seek the solution with form $ \overline{\psi}=\phi(y)e^{i\alpha(x-ct)} $ where $ \alpha $ and c are constants (c is complex in general) so continue derivation 
\begin{align*}
\\-\dfrac{\partial}{\partial t}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)]e^{{\textrm{i}}\alpha(x-ct)}}+U(y)\dfrac{\partial}{\partial x}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)e^{{\textrm{i}}\alpha(x-ct)}]}+U_{yy}(y)\dfrac{\partial}{\partial x}[\phi(y)e^{{\textrm{i}}\alpha(x-ct)}]&=0,\\
\end{align*}
\begin{align*}
\\ \alpha c{\textrm{i}}[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\textrm{i}}\alpha(x-ct)}-\alpha {\textrm{i}}U(y)[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\textrm{i}}\alpha(x-ct)}+\alpha {\textrm{i}}U_{yy} (y)\phi(y)e^{{\textrm{i}}\alpha(x-ct)}&=0,\\
\end{align*}
\begin{align*}
 
 
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Run LaTeX here

[localghost]

First of all, when using the align* environment, you should use it correctly. Typesetting the equations as shown in the image the equation* environment would be sufficient. In case of too long equations you can decrease the font size temporarily.

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Code, edit and compile here:

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\small
\begin{align*}
  -\frac{\partial}{\partial t}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)]e^{{\text{i}}\alpha(x-ct)}}+U(y)\frac{\partial}{\partial x}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)e^{{\text{i}}\alpha(x-ct)}]}+U_{yy}(y)\frac{\partial}{\partial x}[\phi(y)e^{{\text{i}}\alpha(x-ct)}]&=0,\\
  \alpha c{\textrm{i}}[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\text{i}}\alpha(x-ct)}-\alpha {\text{i}}U(y)[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\textrm{i}}\alpha(x-ct)}+\alpha {\textrm{i}}U_{yy} (y)\phi(y)e^{{\textrm{i}}\alpha(x-ct)}&=0,\\
  (c-U(y))(\phi_{yy}(y)-\alpha^{2}\phi(y))+U_{yy}(y)\phi(y)&=0,
\end{align*}
\normalsize
 
 
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Run LaTeX here

Best regards
Thorsten¹