How to use inputenc, fontspec, fontenc, mathdesign and babel to properly render cyrillics and UTF-8 characters?

Question

MWE:

% main.tex
\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage[urw-garamond]{mathdesign}
% \usepackage{fontenc} T1,T2A?
% \usepackage{fontspec} ?
\usepackage[russian,english]{babel}

\begin{document}
“Hello” is the same as “Привет”.
\end{document}

How do I build:

lualatex -synctex=1 -interaction=nonstopmode -file-line-error -recorder main.tex

Log without \usepackage[russian,english]{babel}:

Latexmk: This is Latexmk, John Collins, 26 Dec. 2019, version: 4.67.
Latexmk: All targets () are up-to-date

Output:

Log with \usepackage[russian,english]{babel}:

Latexmk: This is Latexmk, John Collins, 26 Dec. 2019, version: 4.67.
Rule 'lualatex': File changes, etc:
   Changed files, or newly in use since previous run(s):
      '/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.tex'
      'main.tex'
------------
Run number 1 of rule 'lualatex'
------------
------------
Running 'lualatex  -synctex=1 -interaction=nonstopmode -file-line-error -recorder -output-directory="/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions"  "/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.tex"'
------------
Latexmk: applying rule 'lualatex'...
This is LuaTeX, Version 1.10.0 (TeX Live 2019) 
 restricted system commands enabled.
(/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.tex
LaTeX2e <2020-02-02> patch level 5
 L3 programming layer <2020-02-25> (/usr/local/texlive/2019/texmf-dist/tex/latex/base/article.cls
Document Class: article 2019/12/20 v1.4l Standard LaTeX document class
(/usr/local/texlive/2019/texmf-dist/tex/latex/base/size10.clo)) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty

Package inputenc Warning: inputenc package ignored with utf8 based engines.

) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mathdesign.sty (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/ifthen.sty) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdugm/mdugm.cfg) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdugm/mdugm.sty (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdfont.def) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdsffont.def

LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 53.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 56.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 59.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 79.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 102.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 105.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 108.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 128.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 259.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 262.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 265.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 268.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 313.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 316.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 319.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 322.

) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdttfont.def) (/usr/local/texlive/2019/texmf-dist/tex/latex/xkeyval/xkeyval.sty (/usr/local/texlive/2019/texmf-dist/tex/generic/xkeyval/xkeyval.tex (/usr/local/texlive/2019/texmf-dist/tex/generic/xkeyval/xkvutils.tex)))

LaTeX Font Warning: Font shape `TU/mdugm/m/n' undefined
(Font)              using `TU/lmr/m/n' instead on input line 186.

) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/fontenc.sty (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdugm/t1mdugm.fd))) (/usr/local/texlive/2019/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def) (/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.aux

Package babel Warning: Unknown language `russian'. Very likely you
(babel)                requested it in a previous run. Expect some
(babel)                wrong results in this run, which should vanish
(babel)                in the next one. Reported on input line 4.

) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/ts1cmr.fd) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdacmr.fd) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdbcmr.fd) [1{/home/timfayz/.texlive2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] (/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.aux)

LaTeX Font Warning: Some font shapes were not available, defaults substituted.

)
(see the transcript file for additional information)
 411 words of node memory still in use:
   3 hlist, 1 vlist, 1 rule, 2 glue, 3 kern, 1 glyph, 4 attribute, 49 glue_spec, 4 attribute_list, 1 write nodes
   avail lists: 2:15,3:2,4:1,5:21,6:1,7:36,9:7
{/usr/local/texlive/2019/texmf-dist/fonts/enc/dvips/ly1/texnansi.enc}</home/timfayz/.texmf/fonts/type1/urw/garamond/ugmr8a.pfb>
Output written on main.pdf (1 page, 13243 bytes).
SyncTeX written on main.synctex.gz.
Transcript written on main.log.
Latexmk: Log file says output to 'main.pdf'
Rule 'lualatex': File changes, etc:
   Changed files, or newly in use since previous run(s):
      '/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.aux'
      'main.aux'
------------
Run number 2 of rule 'lualatex'
------------
------------
Running 'lualatex  -synctex=1 -interaction=nonstopmode -file-line-error -recorder -output-directory="/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions"  "/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.tex"'
------------
=== TeX engine is 'LuaTeX'
Latexmk: applying rule 'lualatex'...
This is LuaTeX, Version 1.10.0 (TeX Live 2019) 
 restricted system commands enabled.
(/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.tex
LaTeX2e <2020-02-02> patch level 5
 L3 programming layer <2020-02-25> (/usr/local/texlive/2019/texmf-dist/tex/latex/base/article.cls
Document Class: article 2019/12/20 v1.4l Standard LaTeX document class
(/usr/local/texlive/2019/texmf-dist/tex/latex/base/size10.clo)) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/inputenc.sty

Package inputenc Warning: inputenc package ignored with utf8 based engines.

) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mathdesign.sty (/usr/local/texlive/2019/texmf-dist/tex/latex/graphics/keyval.sty) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/ifthen.sty) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdugm/mdugm.cfg) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdugm/mdugm.sty (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdfont.def) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdsffont.def

LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 53.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 56.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 59.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 79.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 102.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 105.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 108.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 128.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 259.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 262.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 265.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 268.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 313.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 316.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 319.


LaTeX Warning: Font shape declaration has incorrect series value `mc'.
               It should not contain an `m'! Please correct it.
               Found on input line 322.

) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdttfont.def) (/usr/local/texlive/2019/texmf-dist/tex/latex/xkeyval/xkeyval.sty (/usr/local/texlive/2019/texmf-dist/tex/generic/xkeyval/xkeyval.tex (/usr/local/texlive/2019/texmf-dist/tex/generic/xkeyval/xkvutils.tex)))

LaTeX Font Warning: Font shape `TU/mdugm/m/n' undefined
(Font)              using `TU/lmr/m/n' instead on input line 186.

) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/fontenc.sty (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdugm/t1mdugm.fd))) (/usr/local/texlive/2019/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def) (/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.aux) (/usr/local/texlive/2019/texmf-dist/tex/latex/base/ts1cmr.fd) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdacmr.fd) (/usr/local/texlive/2019/texmf-dist/tex/latex/mathdesign/mdbcmr.fd) [1{/home/timfayz/.texlive2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] (/home/timfayz/Dropbox/PhD/TeX/RandomDefinitions/main.aux)

LaTeX Font Warning: Some font shapes were not available, defaults substituted.

)
(see the transcript file for additional information)
 411 words of node memory still in use:
   3 hlist, 1 vlist, 1 rule, 2 glue, 3 kern, 1 glyph, 4 attribute, 49 glue_spec, 4 attribute_list, 1 write nodes
   avail lists: 2:15,3:2,4:1,5:21,6:1,7:36,9:7
{/usr/local/texlive/2019/texmf-dist/fonts/enc/dvips/ly1/texnansi.enc}</home/timfayz/.texmf/fonts/type1/urw/garamond/ugmr8a.pfb>
Output written on main.pdf (1 page, 13243 bytes).
SyncTeX written on main.synctex.gz.
Transcript written on main.log.
Latexmk: Log file says output to 'main.pdf'
Latexmk: Summary of warnings from last run of (pdf)latex:
  =====Latex reported missing or unavailable character(s).
=====See log file for details.
=== TeX engine is 'LuaTeX'
Latexmk: All targets () are up-to-date

Output:

Here is what I'm trying to achieve:

I want to use URW Garamond and its mathdesign's version for typing math
I want to have Cyrillic glyphs support (of course, if URW Garamond supports it, if it doesn't - set another font only for the range of Russian characters)
I want to be able to use UTF-8 symbols in both text and math modes
I want to know how to list available fonts in my system (both their conventional names, as you will see in the examples below, and filenames). Or would be even better not only list names but to check if a font supports Russian glyphs.

With that being said I have no idea how to glue all these pieces together :(. What I know so far:

I need the mix of inputenc, fontspec, fontenc, mathdesign, babel in right order with the right options
Reading the logs didn't give me anything useful for googling. I did a lot of trials and a lot readings on Russian websites but it gave me nothing. Seems like people just miraculously get it working.
I don't know if I still need \usepackage[utf8]{inputenc} at preamble. Do I (in 2020)? For I recently got the following Package inputenc Error: inputenc is not designed for xetex or luatex. (I don't remember the circumstances but I saved it for worst)
Seems like babel redefines font afterwords which makes me totally confused. I though it doesn't touch the font settings and we should use fontspec instead.
For the reason above, I have no idea how to properly manage all these peculiar font settings. We have a lot of methods to do the same things. Here is a bunch of commands that influence, explicitly or implicitly, the final font face:

% Method 1
\usepackage{fontspec} 
\setmainfont{EB Garamond}
\setsansfont{CMU Sans Serif}
\setmonofont{...}

% Method 2
\usepackage{unicode-math}
\setmathfont{texgyrepagella-math.otf}

% Method 3
\usepackage{ebgaramond} % just an example at hand, I encountered other packages that redefine typefaces as well

% Method 4
\babelfont{rm}{DejaVu Serif} % ?

Environment:

$ lualatex -v
This is LuaTeX, Version 1.10.0 (TeX Live 2019)
$ tlmgr version
tlmgr revision 53842 (2020-02-19 08:28:40 +0100)
tlmgr using installation: /usr/local/texlive/2019
$ latex -v
pdfTeX 3.14159265-2.6-1.40.20 (TeX Live 2019)
kpathsea version 6.3.1
$ latexmk -v
Latexmk, John Collins, 26 Dec. 2019. Version 4.67

Packages that I explicitly installed (see only uncommented lines):

tlmgr update --self
tlmgr install \
    collection-basic \
        # luatex \
    collection-latex \
    collection-latexrecommended \
        # fontspec \
    collection-luatex \
        # luaotfload \
        # lualatex-math \
    collection-fontsrecommended \
        # cm-super \ # cyrillic support (T1 encoding)
    # collection-binextra \
        latexmk \
        texliveonfly \ # resolve deps automagically
    # collection-pictures \
        pgfplots \
    # collection-latexextra \
        needspace \
        mdframed \
        multirow \ # to create cells spanning multiple rows
    # collection-bibtexextra \
        biblatex biber \ # modern bibliography engine + backend
    # collection-fontsextra \
        ebgaramond \ # favorite serif font
        mathdesign \ # favorite math + normal text font
        ly1 \ # resolve missing texnansi.enc
    # collection-langcyrillic \
        babel-russian \ # russian support

urw-garamond was installed manually as suggested here

Uff. Well you shouldn't use luatex if you want to use urw garamond. — Ulrike Fischer, Mar 18, 2020 at 18:38
Welcome to this site! As an aside, thanks for taking the time to ask a question with a small example, and a lot of additional detail. — ShreevatsaR, Mar 18, 2020 at 18:52
Related: Cyrillic in math mode: tex.stackexchange.com/questions/201239/… . tex.stackexchange.com/questions/14633/… . tex.stackexchange.com/questions/59181/… — Cicada, Mar 19, 2020 at 12:34
Big question set! Equivalent to 'How to use latex?'. One element at a time: First decide if you want to use Unicode and system fonts (fontspec for fonts, babel or polyglossia for language and hyphenation, compile with xelatex or lualatex), or use legacy fonts (compile with pdflatex). Second element: font coverage. Third element: Cyrillic math. — Cicada, Mar 19, 2020 at 12:43

Cicada · Accepted Answer · 2020-03-20 10:10:54Z

Here is an example, to start you off on the Unicode track.

I will try and add to it over the next days and weeks. The answers to all the questions are almost like a set of mini tutorials.

Starting with general text:

font=Noto Serif; language=Tatar; textsource=Wikipedia; compiler=xelatex (or lualatex); texttopic=solar system; hyphenation-pattern=russian, via babel.

Exercise: Try the example without babel, and see what happens to the hyphenation.

\documentclass[12pt]{article}
\usepackage{fontspec}
\setmainfont{Noto Serif}
\usepackage[russian]{babel}%hyphenation
\begin{document}
“Hello” is the same as “Привет”.
\bigskip

tt Wikipedia
\section*{Кояш системасы}

\textbf{Кояш системасы} — Кояш йолдызы һәм аның тирәсендә әйләнә торган табигый галәми объектлар белән планеталар системасы.

Кояш системасының Кояштан тыш объектларының төп массасы сигез аерым планетада була. Алар эклиптика яссылыкта түгәрәккә якын орбиталар буенча хәрәкәт итәләр. Дүрт кечерәк эчке планета: Меркурий, Чулпан, Җир һәм Марс (җирсыман планеталар) гомумән силикатлардан һәм металлардан гыйбарәт була. Дүрт зуррак тышкы планета: Юпитер, Сатурн, Уран һәм Нептун (зур газлы планеталар) төп өлешендә водородтан һәм гелийдан гыйбарәт була һәм җирсыман планеталардан күпкә авыррак. 

\end{document}

How to find a font

The fc-list utility is useful: fc-list :lang=zh-cn finds fonts that support Chinese (How can I list all the Chinese fonts I have installed? (Ubuntu, TexLive)).

An experiment: on my system (Windows), doing fc-list :lang=tt-tt, to find fonts supporting Tatar, produces a list which includes PT Sans font. Using that font as a test case in the MWE produces this:

which looks alright, actually, from the glyph-coverage point of view, as far as I can tell (I have yet to learn Tatar).

There are other ways besides: looking in the font itself with a font editor or character map; listing font-features with xelatex/fontspec code (questions on this site); using free apps like BabelPad to examine a font's coverage of a Unicode block, or a Unicode block's coverage by which fonts; and so on.

Davislor · Accepted Answer · 2021-08-16 20:15:37Z

Some of those packages are for different engines, and you wouldn’t be able to use them together. In LuaLaTeX or XeLaTeX, you’d only use Unicode fonts.

You can load a Garamond font family through unicode-math, but there is already a package that does this for you, fontsetup. It probably suffices if you need only short phrases in Russian:

\documentclass{article}
\tracinglostchars=3 % Make it an error if a character is missing from the current font.
\usepackage[paperwidth=10cm]{geometry} % Format the MWE for TeX.SX.
\usepackage{mathtools}
\usepackage[russian,english]{babel}
\usepackage[ebgaramond]{fontsetup}

\newcommand\iu{\i} % The imaginary unit.
\newcommand\diff{\mathop{}\symup{d}} % The differential operator.

\begin{document}
Pafnuty Chebyshev (Пафну́тий Чебышёв) proved that the differential equation

\begin{gather}
  \left(1 - x^2\right) \frac{\diff^2 y}{\diff x^2} +
     \frac{\diff y}{\diff x} +
     \alpha^2 y
   = 0 \\
  \intertext{has the solution}
  \begin{aligned}
    y = &c_1 \cosh \left[  \alpha \ln \left( x + \sqrt{x^2 - 1} \right)\right] + \\
        &\iu c_2 \sinh \left[ \alpha \ln \left(x+ \sqrt{x^2 - 1} \right)\right]
  \end{aligned}
\end{gather}
\end{document}

If you want to include complete sentences in Russian, with correct hyphenation, you can use this template in LuaLaTeX, which detects the language you are typing in and sets the font and hyphenation rules accordingly:

\documentclass{article}
\tracinglostchars=3 % Make it an error if a character is missing from the current font.
\usepackage[paperwidth=10cm]{geometry} % Format the MWE for TeX.SX.
\usepackage{mathtools}
\usepackage[english]{babel}
\usepackage{unicode-math}
\usepackage{microtype}

\babelprovide[import, onchar=fonts ids]{russian}
\babelfont{rm}
          {EBGaramond}
\setmathfont{Garamond-Math}

\newcommand\iu{\i} % The imaginary unit.
\newcommand\diff{\mathop{}\symup{d}} % The differential operator.

\begin{document}
Pafnuty Chebyshev (Пафну́тий Чебышёв) proved that the differential equation

\begin{gather}
  \left(1 - x^2\right) \frac{\diff^2 y}{\diff x^2} +
     \frac{\diff y}{\diff x} +
     \alpha^2 y
   = 0 \\
  \intertext{has the solution}
  \begin{aligned}
    y = &c_1 \cosh \left[  \alpha \ln \left( x + \sqrt{x^2 - 1} \right)\right] + \\
        &\iu c_2 \sinh \left[ \alpha \ln \left(x+ \sqrt{x^2 - 1} \right)\right]
  \end{aligned}
\end{gather}

Пафну́тий Льво́вич Чебышёв—русский математик и механик,
основоположникпетербургской математической школы, академик Петербургской
академии наук (адъюнкт с 1853 года, экстраординарный академик с 1859 года)
и ещё 24 академий мира.
\end{document}

If your publisher still, in 2021 or beyond, is forcing you to use 8-bit fonts in PDFLaTeX, this template should work: This loads a free version of Garamond that supports Cyrillic, Garamond Libre, as the text fonts over the math fonts in mathdesign.

\documentclass{article}
\tracinglostchars=3 % Make it an error if a character is missing from the current font.
\usepackage[T2A,T1]{fontenc}
\usepackage[utf8]{inputenc} % The default since 2018.
\usepackage[paperwidth=10cm]{geometry} % Format the MWE for TeX.SX.
\usepackage{mathtools}
\usepackage[russian,english]{babel}
\usepackage{microtype}
\usepackage[garamond]{mathdesign}
\usepackage{garamondlibre}

\newcommand\iu{\textit{\i}} % The imaginary unit.
\newcommand\diff{\mathop{}\mathrm{d}} % The differential operator.

\begin{document}
Pafnuty Chebyshev (\foreignlanguage{russian}{Пафн\'{у}тий Чебышёв}) proved that
the differential equation
\begin{gather}
  \left(1 - x^2\right) \frac{\diff^2 y}{\diff x^2} +
     \frac{\diff y}{\diff x} +
     \alpha^2 y
   = 0 \\
  \intertext{has the solution}
  \begin{aligned}
    y = &c_1 \cosh \left[  \alpha \ln \left( x + \sqrt{x^2 - 1} \right)\right] + \\
        &\iu c_2 \sinh \left[ \alpha \ln \left(x+ \sqrt{x^2 - 1} \right)\right]
  \end{aligned}
\end{gather}

\begin{otherlanguage}{russian}
Пафн\'{у}тий Льв\'{о}вич Чебышёв—русский математик и механик,
основоположникпетербургской математической школы, академик Петербургской
академии наук (адъюнкт с 1853 года, экстраординарный академик с 1859 года)
и ещё 24 академий мира.
\end{otherlanguage}
\end{document}

There are a few workarounds needed here. First, PDFLaTeX cannot automatically detect the language you use, so this version of the document needs explicit tagging. Second, PDFLaTeX cannot handle combining accents such as U+0301, but there are no precomposed letters such as У́ in Unicode, so you must write them as something like \'{У}.

You can remove the extra line before \begin{gather} if you want. — Davislor, Aug 16, 2021 at 19:48
I know that many of you have your own preferred style for the differential operator and imaginary unit, so please feel more than free to redefine \diff and \iu to your heart’s content. — Davislor, Aug 16, 2021 at 19:53

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How to use inputenc, fontspec, fontenc, mathdesign and babel to properly render cyrillics and UTF-8 characters?

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How to use inputenc, fontspec, fontenc, mathdesign and babel to properly render cyrillics and UTF-8 characters?

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