#環境
OS：AmazonLinux2
Ryby：ruby 2.6.3p62 (2019-04-16 revision 67580) [x86_64-linux]
Rails：Rails 5.0.0

#問題
データベースをmysqlに指定してRailsアプリケーションを新規作成した際、mysql2のGemのインストール中にエラーが発生した。

結論

DBクライアントというパッケージをインストールしていなかったことが原因だった。

#やったこと
以下コマンドで、データベースをmysqlに指定して、新規アプリケーションを作成
$ rails new (アプリケーション名) -d mysql

$ rails new shift-management -d mysql
      
~省略~

Fetching mysql2 0.4.10
Installing mysql2 0.4.10 with native extensions
Gem::Ext::BuildError: ERROR: Failed to build gem native extension.

    current directory: /home/ec2-user/.rvm/gems/ruby-2.6.3/gems/mysql2-0.4.10/ext/mysql2
/home/ec2-user/.rvm/rubies/ruby-2.6.3/bin/ruby -I /home/ec2-user/.rvm/rubies/ruby-2.6.3/lib/ruby/site_ruby/2.6.0 -r ./siteconf20201203-7896-3nmivb.rb extconf.rb
checking for rb_absint_size()... yes
checking for rb_absint_singlebit_p()... yes
checking for ruby/thread.h... yes
checking for rb_thread_call_without_gvl() in ruby/thread.h... yes
checking for rb_thread_blocking_region()... no
checking for rb_wait_for_single_fd()... yes
checking for rb_hash_dup()... yes
checking for rb_intern3()... yes
checking for rb_big_cmp()... yes
checking for mysql_query() in -lmysqlclient... yes
checking for mysql.h... no
checking for mysql/mysql.h... no
-----
mysql.h is missing. You may need to 'apt-get install libmysqlclient-dev' or 'yum install mysql-devel', and try again.
-----
*** extconf.rb failed ***
Could not create Makefile due to some reason, probably lack of necessary
libraries and/or headers.  Check the mkmf.log file for more details.  You may
need configuration options.

Provided configuration options:
        --with-opt-dir
        --without-opt-dir
        --with-opt-include
        --without-opt-include=${opt-dir}/include
        --with-opt-lib
        --without-opt-lib=${opt-dir}/lib
        --with-make-prog
        --without-make-prog
        --srcdir=.
        --curdir
        --ruby=/home/ec2-user/.rvm/rubies/ruby-2.6.3/bin/$(RUBY_BASE_NAME)
        --with-mysql-dir
        --without-mysql-dir
        --with-mysql-include
        --without-mysql-include=${mysql-dir}/include
        --with-mysql-lib
        --without-mysql-lib=${mysql-dir}/lib
        --with-mysql-config
        --without-mysql-config
        --with-mysql-dir
        --without-mysql-dir
        --with-mysql-include
        --without-mysql-include=${mysql-dir}/include
        --with-mysql-lib
        --without-mysql-lib=${mysql-dir}/lib
        --with-mysqlclientlib
        --without-mysqlclientlib

To see why this extension failed to compile, please check the mkmf.log which can be found here:

  /home/ec2-user/.rvm/gems/ruby-2.6.3/extensions/x86_64-linux/2.6.0/mysql2-0.4.10/mkmf.log

extconf failed, exit code 1

Gem files will remain installed in /home/ec2-user/.rvm/gems/ruby-2.6.3/gems/mysql2-0.4.10 for inspection.
Results logged to /home/ec2-user/.rvm/gems/ruby-2.6.3/extensions/x86_64-linux/2.6.0/mysql2-0.4.10/gem_make.out

An error occurred while installing mysql2 (0.4.10), and Bundler cannot continue.
Make sure that `gem install mysql2 -v '0.4.10' --source 'https://rubygems.org/'` succeeds before bundling.

In Gemfile:
  mysql2
         run  bundle exec spring binstub --all
bundler: command not found: spring
Install missing gem executables with `bundle install`

mysql2がインストールできないと言われる

原因

どうやらDBクライアントをインストールしていないことが原因だった
参考：AmazonLinux2にMariaDBをインストールする

解決策

DBクライアントをインストール（パッケージインストール）

$ sudo yum install mariadb-devel
Loaded plugins: extras_suggestions, langpacks, priorities, update-motd
220 packages excluded due to repository priority protections
Resolving Dependencies
--> Running transaction check
---> Package mariadb-devel.x86_64 3:10.2.10-2.amzn2.0.3 will be installed
--> Finished Dependency Resolution

Dependencies Resolved

================================================================================================================================================================================================
 Package                                 Arch                             Version                                            Repository                                                    Size
================================================================================================================================================================================================
Installing:
 mariadb-devel                           x86_64                           3:10.2.10-2.amzn2.0.3                              amzn2extra-lamp-mariadb10.2-php7.2                           1.0 M

Transaction Summary
================================================================================================================================================================================================
Install  1 Package

Total download size: 1.0 M
Installed size: 4.5 M
Is this ok [y/d/N]: y
Downloading packages:
mariadb-devel-10.2.10-2.amzn2.0.3.x86_64.rpm                                                                                                                             | 1.0 MB  00:00:00     
Running transaction check
Running transaction test
Transaction test succeeded
Running transaction
  Installing : 3:mariadb-devel-10.2.10-2.amzn2.0.3.x86_64                                                                                                                                   1/1 
  Verifying  : 3:mariadb-devel-10.2.10-2.amzn2.0.3.x86_64                                                                                                                                   1/1 

Installed:
  mariadb-devel.x86_64 3:10.2.10-2.amzn2.0.3                                                                                                                                                    

Complete!

インストール完了（mysql-develでも同じみたい）

もう一度bundle installすると

$ bundle install 
The dependency tzinfo-data (>= 0) will be unused by any of the platforms Bundler is installing for. Bundler is installing for ruby but the dependency is only for x86-mingw32, x86-mswin32, x64-mingw32, java. To add those platforms to the bundle, run `bundle lock --add-platform x86-mingw32 x86-mswin32 x64-mingw32 java`.
Fetching gem metadata from https://rubygems.org/............
Fetching gem metadata from https://rubygems.org/.
Resolving dependencies....
Using rake 13.0.1
Using concurrent-ruby 1.1.7
Using i18n 1.8.5
Using minitest 5.14.2
Using thread_safe 0.3.6
Using tzinfo 1.2.8
Using activesupport 5.0.7.2
Using builder 3.2.4
Using erubis 2.7.0
Using mini_portile2 2.4.0
Using nokogiri 1.10.10
Using rails-dom-testing 2.0.3
Using crass 1.0.6
Using loofah 2.8.0
Using rails-html-sanitizer 1.3.0
Using actionview 5.0.7.2
Using rack 2.2.3
Using rack-test 0.6.3
Using actionpack 5.0.7.2
Using nio4r 2.5.4
Using websocket-extensions 0.1.5
Using websocket-driver 0.6.5
Using actioncable 5.0.7.2
Using globalid 0.4.2
Using activejob 5.0.7.2
Using mini_mime 1.0.2
Using mail 2.7.1
Using actionmailer 5.0.7.2
Using activemodel 5.0.7.2
Using arel 7.1.4
Using activerecord 5.0.7.2
Using bindex 0.8.1
Using bundler 1.17.3
Using byebug 11.1.3
Using coffee-script-source 1.12.2
Using execjs 2.7.0
Using coffee-script 2.4.1
Using method_source 1.0.0
Using thor 1.0.1
Using railties 5.0.7.2
Using coffee-rails 4.2.2
Using ffi 1.13.1
Using jbuilder 2.10.1
Using jquery-rails 4.4.0
Using rb-fsevent 0.10.4
Using rb-inotify 0.10.1
Using listen 3.0.8
Fetching mysql2 0.4.10
Installing mysql2 0.4.10 with native extensions
Fetching puma 3.12.6
Installing puma 3.12.6 with native extensions
Fetching sprockets 3.7.2
Installing sprockets 3.7.2
Using sprockets-rails 3.2.2
Fetching rails 5.0.7.2
Installing rails 5.0.7.2
Fetching sass-listen 4.0.0
Installing sass-listen 4.0.0
Fetching sass 3.7.4
Installing sass 3.7.4
Fetching tilt 2.0.10
Installing tilt 2.0.10
Fetching sass-rails 5.0.7
Installing sass-rails 5.0.7
Fetching spring 2.1.1
Installing spring 2.1.1
Fetching spring-watcher-listen 2.0.1
Installing spring-watcher-listen 2.0.1
Fetching turbolinks-source 5.2.0
Installing turbolinks-source 5.2.0
Fetching turbolinks 5.2.1
Installing turbolinks 5.2.1
Fetching uglifier 4.2.0
Installing uglifier 4.2.0
Fetching web-console 3.7.0
Installing web-console 3.7.0
Bundle complete! 15 Gemfile dependencies, 62 gems now installed.
Use `bundle info [gemname]` to see where a bundled gem is installed.
Post-install message from sass:

Ruby Sass has reached end-of-life and should no longer be used.

* If you use Sass as a command-line tool, we recommend using Dart Sass, the new
  primary implementation: https://sass-lang.com/install

* If you use Sass as a plug-in for a Ruby web framework, we recommend using the
  sassc gem: https://github.com/sass/sassc-ruby#readme

* For more details, please refer to the Sass blog:
  https://sass-lang.com/blog/posts/7828841

無事mysql2がインストールされました。
以下に、Railsアプリケーションの作成時の手順を書いているので参考にしてみてください

【AmazonLinux2】Railsアプリケーション新規作成 rake db:createまで