# How can I get my columns to align vertically with multicols?

For some reason there's this ugly blank line in the left column that I just can;t get rid of. Here's what Ive got typed out:

\begin{multicols}{2}
$$y_{1}(t)$$:
\noindent
\begin{align*}
t^2 y''-2y&=t^2 y_{1}''-2y_{1}\\
&=t^2(2)-2t^{2}\\
&=2t^{2}-2t^{2}\\
&=0
\end{align*}

\columnbreak

$$y_{2}(t)$$:
\begin{align*}
t^2 y''-2y&=t^2 y_{2}''-2y_{2}\\
&=t^{2}\left(\frac{2}{t^3}\right)-\frac{2}{t}\\
&=\frac{2}{t}-\frac{2}{t}\\
&=0
\end{align*}
\end{multicols}


What could I do to fix it? I've never really run into this issue before

• You have placed \noindent just before a math display environment. That has the effect of starting a new paragraph, but the display math then starts a new "block", leaving a blank line. If you want the display block flush left, use flalign as the environment. Sep 23 at 3:25

If you want to use an approach similar to the one you're using now, I would use \raggedcolumns so that the multicols environment doesn't try to vertically balance the shorter material in the left column.

\documentclass{article}
\usepackage{amsmath,mathtools}
\usepackage{multicol}
\begin{document}

\begin{multicols}{2}
\raggedcolumns
\noindent$$y_{1}(t)$$:
\begin{align*}
t^2 y''-2y&=t^2 y_{1}''-2y_{1}\\
&=t^2(2)-2t^{2}\\
&=2t^{2}-2t^{2}\\
&=0
\end{align*}

\columnbreak

\noindent$$y_{2}(t)$$:
\begin{align*}
t^2 y''-2y&=t^2 y_{2}''-2y_{2}\\
&=t^{2}\left(\frac{2}{t^3}\right)-\frac{2}{t}\\
&=\frac{2}{t}-\frac{2}{t}\\
&=0
\end{align*}
\end{multicols}

\end{document}


However, in this case, I'm not sure why you need columns for this at all. If your equations don't need to be separately numbered, you can use a single align* environment, as this environment supports multiple sets of aligned formulas next to each other.

Alternatively, you could put each group inside an aligned environment; then the larger spacing (because of the fractions) in the right group won't be applied to the left group as well.

Here's code for both approaches:

\documentclass{article}
\usepackage{amsmath,mathtools}
\begin{document}

With one big align environment:

\begin{align*}
& \mathrlap{y_{1}(t):} & & & & \mathrlap{y_{2}(t):} & & & \\
& &    t^2 y''-2y &=t^2 y_{1}''-2y_{1} &&& t^2 y''-2y&=t^2 y_{2}''-2y_{2}             \\
& &               &=t^2(2)-2t^{2}      &&&           &=t^{2}\left(\frac{2}{t^3}\right)-\frac{2}{t} \\
& &               &=2t^{2}-2t^{2}      &&&           &=\frac{2}{t}-\frac{2}{t} \\
& &               &=0                  &&&           &=0
\end{align*}

With two aligned environments inside an align* environment:

\begin{align*}
y_{1}(t): & & y_{2}(t): \\
%
& \begin{aligned}[t]
t^2 y''-2y&=t^2 y_{1}''-2y_{1}\\
&=t^2(2)-2t^{2}\\
&=2t^{2}-2t^{2}\\
&=0
\end{aligned}
&
&
\begin{aligned}[t]
t^2 y''-2y&=t^2 y_{2}''-2y_{2}\\
&=t^{2}\left(\frac{2}{t^3}\right)-\frac{2}{t}\\
&=\frac{2}{t}-\frac{2}{t}\\
&=0
\end{aligned}
\end{align*}

\end{document}


You needn't multicol package. You can construct the same by TeX primitive \hbox and two \vtops inside it:

\hbox to\hsize{%
\vtop{smaller \hsize, left material}\hss
\vtop{smaller \hsize, right material}}


\hbox to\hsize{%
\vtop{\hsize=.45\hsize
$$y_{1}(t)$$:
\begin{align*}
t^2 y''-2y&=t^2 y_{1}''-2y_{1}\\
&=t^2(2)-2t^{2}\\
&=2t^{2}-2t^{2}\\
&=0
\end{align*}
}\hss
\vtop{\hsize=.45\hsize
$$y_{2}(t)$$:
\begin{align*}
t^2 y''-2y&=t^2 y_{2}''-2y_{2}\\
&=t^{2}\left(\frac{2}{t^3}\right)-\frac{2}{t}\\
&=\frac{2}{t}-\frac{2}{t}\\
&=0
\end{align*}
}}


I'd use two minipages, so you can better control the horizontal and vertical alignment.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

Some text before the display, long enough to wrap across lines.
Perhaps this is enough.
\begin{minipage}[t]{0.45\displaywidth} \begin{aligned}[t] &y_{1}(t)\,{:}\\ &\quad \begin{aligned} t^2 y''-2y&=t^2 y_{1}''-2y_{1}\\ &=t^2(2)-2t^{2}\\ &=2t^{2}-2t^{2}\\ &=0 \end{aligned} \end{aligned} \end{minipage} \begin{minipage}[t]{0.45\displaywidth} \begin{aligned}[t] &y_{2}(t)\,{:} \\ &\quad \begin{aligned} t^2 y''-2y&=t^2 y_{2}''-2y_{2}\\ &=t^{2}\left(\frac{2}{t^3}\right)-\frac{2}{t}\\ &=\frac{2}{t}-\frac{2}{t}\\ &=0 \end{aligned} \end{aligned} \end{minipage}
Some text below the display, long enough to wrap across lines.
Perhaps this is enough.

\end{document}


You may insert your equation systems in table, for example tblr defined in the tabularray package:

\documentclass[11pt]{book}
\usepackage{tabularray}
\UseTblrLibrary{amsmath, varwidth}

\begin{document}
\begin{table}[htb]
\begin{tblr}{colsep =0pt,
colspec={X[c, mode=math] c  X[c, mode=math]},
row{1} ={l}
}
%
\begin{aligned}[t]  % <---
t^2 y''-2y&=t^2 y_{1}''-2y_{1}\\
&=t^2(2)-2t^{2}\\
&=2t^{2}-2t^{2}\\
&=0
\end{aligned}   &       &  \begin{aligned}[t]˛ % <---
t^2 y''-2y&=t^2 y_{2}''-2y_{2}\\
&=t^{2}\left(\frac{2}{t^3}\right)-\frac{2}{t}\\
&=\frac{2}{t}-\frac{2}{t}\\
&=0
\end{aligned}
\end{tblr}
\end{table}
\end{document}