Question: Just typing them directly does not work.

Just like `\alpha` is different from `α`, `ю` produces a non-italic letters that also don't follow correct spacing:  

`Ю + 1` produces  

[![Ю + 1 but the plus is too far to the right](https://i.stack.imgur.com/rcP4U.png)](https://i.stack.imgur.com/rcP4U.png)

Answer: 
You can define a new math symbol font.

```latex
\documentclass{article}
\usepackage{cmap}
\usepackage[T2A,T1]{fontenc}

\DeclareSymbolFont{cyrillic}{T2A}{cmr}{m}{it}
\SetSymbolFont{cyrillic}{bold}{T2A}{cmr}{bx}{it}

\DeclareMathSymbol{\mYu}{\mathord}{cyrillic}{222}

\begin{document}

$\mYu+1$

{\boldmath$\mYu+1$}

\end{document}

```

[![enter image description here](https://i.stack.imgur.com/g8RBm.png)](https://i.stack.imgur.com/g8RBm.png)

Look in your system for the file `t2aenc.def` in order to find the numeric code. The uppercase Ю is called `\CYRYU`.

With `cmap`, the character is copied as itself from the PDF file.
You can use any text-mode symbol and formatting commands in math mode with `\textnormal` from `amsmath`. Here’s [an answer I gave](https://tex.stackexchange.com/questions/542007/cyrillic-letters-acm-template) to a similar question a few months ago. In this case, you’d want `\textit{ю}` if you want it to appear bold in a bold header, or `\textnormal{\itshape ю}` to have it always appear as medium italic.

The `fontspec` package gives you another option. It sets `\mathrm`, `\mathit`, etc. to use the main text font, or another you provide. If you set it to a font that supports Cyrillic (such as `\setmathrm{CMU Serif}[Ligatures={Common,TeX}]`), you can use `\mathrm{ю}`, `\mathit{ю}`, and so on.