Your best bet is to use a cross platform library like Qt or something like that. Qt has a nice class called QDesktopServices which you can use to do it:
QDesktopServices::openUrl(QUrl("http://google.com", QUrl::TolerantMode));
According to the documentation:
Opens the given url in the appropriate Web browser for the user's
desktop environment, and returns true if successful; otherwise returns
false.
Do note that this will add an dependency on Qt for all your platforms for what might be a very trivial task. It is best that you use custom code for each platform and set compiler directives to see which operating system you are on and run the browser launching code according to that.
Like, if it is being compiled on windows, you could just compile ShellExecute function, if it is being run on Linux, then depending on the desktop environment you could run the appropriate command.
But, if you are really making a cross platform application, a dependency like Qt would not be bad as it will help with a lot of cross-platform stuff (like keeping an icon in the system tray, multimedia playback etc.).
Without a library, there is no standard-C++ way to do it that will run on all platforms.