@PaulGessler So do you mean that it should be like that?
 \begin{multline}
y'=y+4 \pi \cos(4 \pi t)y \Rightarrow y'=(1+ 4 \pi \cos(4 \pi t))y \cap
\Rightarrow \frac{dy}{dt}=(1+ 4 \pi \cos(4 \pi t))y \cap
\Rightarrow \frac{dy}{y}=(1+ 4 \pi \cos(4 \pi t)) dt

\end{multline}

\documentclass{article}
\usepackage{amsmath}

\newcommand{\diff}{\mathop{}\!d}

\begin{document}

\begin{multline*}
\biggl|
  \int_{\Omega}
    \lvert \nabla u_{n}\rvert^{p-2}
    \nabla u_{n}\cdot\nabla(u_{n}-u)
  \diff x
  - \lambda_{1}
  \int_{\Omega}
    \lvert u_{n}\rvert^{p-2}
    u_{n}(u_{n}-u)
  \diff x
  \\
  -\int_{\Omega}
     f(x,u_{n})\,(u_{n}-u)
   \diff x
  +\int_{\Omega}
     h(u_{n}-u)
   \diff x
\biggr|
\le \varepsilon_{n}\lVert u_{n}-u\rVert
\end{multline*}

\end{document}

%%   filename  = "amstex.tex",
%%   version   = "2.2",
%%   date      = "2001/10/04",

	If the Tao is great, then the operating system is great.  If the
operating system is great, then the compiler is great.  If the compiler
is great, then the application is great.  If the application is great, then
the user is pleased and there is harmony in the world.
	The Tao gave birth to machine language.  Machine language gave birth
to the assembler.
	The assembler gave birth to the compiler.  Now there are ten thousand
languages.
	Each language has its purpose, however humble.  Each language

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