Solving Line Breaking Issues in LATEX

[evinda]

Hello! (Wave)

I am writing a text in LATEX.
Since the equalities I wrote are longer than the paper's size, I tried to break the line as follows, but it failed.
[m]\begin{multline} [/m]
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
[m]\end{multline} [/m]Why? What could I do?

 

[Evgeny.Makarov]

You should probably use [m]\\[/m] instead of [m]\cap[/m].

Personally, I think alignment works better here.

\begin{align}
&y'=y+4 \pi \cos(4 \pi t)y\\
&\quad\implies y'=(1+ 4 \pi \cos(4 \pi t))y\\
&\quad\implies \frac{dy}{dt}=(1+ 4 \pi \cos(4 \pi t))y\\
&\quad\implies \frac{dy}{y}=(1+ 4 \pi \cos(4 \pi t)) dt
\end{align}

 

[evinda]

You should probably use [m]\\[/m] instead of [m]\cap[/m].

Yes, this would work...

Personally, I think alignment works better here.

\begin{align}
&y'=y+4 \pi \cos(4 \pi t)y\\
&\quad\implies y'=(1+ 4 \pi \cos(4 \pi t))y\\
&\quad\implies \frac{dy}{dt}=(1+ 4 \pi \cos(4 \pi t))y\\
&\quad\implies \frac{dy}{y}=(1+ 4 \pi \cos(4 \pi t)) dt
\end{align}

I tried it and I got this:
View attachment 4214Why do the numbers appear at the right side of each equality? How could we get rid of them?

 

[Evgeny.Makarov]

To avoid equation numbers, use the environment [m]align*[/m] instead of [m]align[/m]. There is also an analogous [m]aligned[/m] environment that does not occupy the whole width of the line and can be used as a subformula in other formulas. You can read about these environments in the User’s Guide for the amsmath Package (search for it).