The DO-178B guidelines apply to civil aviation for aircraft, helicopters and engines as mandated by the Federal Aviation Regulations. The guidelines also apply to the systems and equipment that utilize software or airborne electronic hardware used in aviation.
For systems and equipment using software to fulfill a safety related aircraft function. FAA Advisory Circular 20-115B cites RTCA/DO-178B as a means of compliance to the Federal Aviation Regulations Part 21, 23, 25, 27, 29 and 33. DO-178B is used for all new software development as well as for software changes to legacy systems containing software. The FAA defines DO-178B as a means, but not the only means of compliance to the Federal Aviation Regulations. It is an extremely rare exception that an alternative means of compliance is used for software in avionics applications.
Yes, an aircraft manufacturer can do the software development and verification and have company DERs (Designated Engineering Representative) perform the compliance findings for the software. The resources would need to be appropriately qualified and skilled for the tasks. The company DER would need the appropriate delegation and authorization.