This is soultion how to fix no splash screen in Ubuntu after nvidia proprietary driver installation. It's no matter what Ubuntu version you use, it should work anyway. (TESTED ON 14.04)

• Open your terminal and type:

  sudo apt-get install v86d (TEST WITHOUT)

• Then:

  sudo gedit /etc/default/grub

• Find this line:

  #GRUB_GFXMODE=640x480

• Add below (of course choose your resolution):

  GRUB_GFXMODE=1024x768x32 (TRY WITHOUT OR DIFFERENT BIT DEPTH) GRUB_GFXPAYLOAD_LINUX=1920x1080x32 (YOU CAN ALSO USE THE KEEP OPTION)

• Save file and type in terminal:

  echo FRAMEBUFFER=y | sudo tee /etc/initramfs-tools/conf.d/splash (ALLOWS TO AVOID THAT THE SPLASH SCREEN IS DISPLAYED FOR A FEW SECONDS)

  sudo update-initramfs -u sudo update-grub2

For all those who complain about the presence of black borders in "plymouth", try to make these changes before installing the nvidia driver or switch back from nvidia to nouveau and from nouveau to nvidia. Kernel update from the Software Updater? It happened to me; I don't know if it matters. I don't know for which of these reasons, but after a few reboots, the black borders are gone.

UPDATE

discovered the secret: during all these beautiful things, something strange happened.

glxinfo | grep vendor
server glx vendor string: SGI
client glx vendor string: Mesa Project and SGI
OpenGL vendor string: nouveau