How to Change /etc/resolv.conf on Ubuntu 18 with systemd-resolved

Issue: manually changing /etc/resolv.conf does not work long term because there is a daemon systemd-resolved that is automatically updating that file and overriding our changes.

Solution: update the configuration of systemd-resolved instead

man systemd-resolved

The DNS servers contacted are determined from the global settings in /etc/systemd/resolved.conf, the per-link static settings in
       /etc/systemd/network/*.network files, the per-link dynamic settings received over DHCP and any DNS server information made available by
       other system services. See resolved.conf(5) and systemd.network(5) for details about systemd's own configuration files for DNS servers. To
       improve compatibility, /etc/resolv.conf is read in order to discover configured system DNS servers, but only if it is not a symlink to
       /run/systemd/resolve/stub-resolv.conf or /run/systemd/resolve/resolv.conf (see below).

In this example we will replace the default to perform DNS queries via google DNS servers 8.8.8.8 and 8.8.4.4

add or update the DNS line in the file /etc/systemd/resolved.conf, the DNS servers are simply separated with a space:

DNS=8.8.8.8 8.8.4.4

This is how a diff of the original config and the modified file looks like:

diff --git a/systemd/resolved.conf b/systemd/resolved.conf
index 3758089..649a7c4 100644
--- a/systemd/resolved.conf
+++ b/systemd/resolved.conf
@@ -12,7 +12,7 @@
 # See resolved.conf(5) for details

 [Resolve]
-#DNS=
+DNS=8.8.8.8 8.8.4.4
 #FallbackDNS=
 #Domains=
 #LLMNR=no

Restart resolved

sudo service systemd-resolved restart

Notice that this will not change the content of the file /etc/resolv.conf but it will change the DNS servers used by the daemon listening on 127.0.0.53

cat /etc/resolv.conf

# This file is managed by man:systemd-resolved(8). Do not edit.
#
# This is a dynamic resolv.conf file for connecting local clients to the
# internal DNS stub resolver of systemd-resolved. This file lists all
# configured search domains.
#
# Run "systemd-resolve --status" to see details about the uplink DNS servers
# currently in use.
#
# Third party programs must not access this file directly, but only through the
# symlink at /etc/resolv.conf. To manage man:resolv.conf(5) in a different way,
# replace this symlink by a static file or a different symlink.
#
# See man:systemd-resolved.service(8) for details about the supported modes of
# operation for /etc/resolv.conf.

nameserver 127.0.0.53
options edns0
search openstacklocal