How do I update my opengl version on both linux and windows? How does this work? Do I need to change the implementation?
Just update your graphics driver by downloading a new version and installing it. Google "VENDOR driver download" (substituting NVidia, AMD, or Intel for VENDOR) to get a link to their download page.
On Linux you may have additional options if your distribution's package installer has vendor graphics drivers available in it.
On Linux to see which vendor's drivers you need (and which GPU you have installed), run: