My washing machine outflow hose goes into an open pvc pipe that is attached to my main drain.this pipe can't seem to handle the volume of water even though a snake goes through and a garden hose at full blast is no problem. This is a recent development. Any answers?

Is the washing machine new? Newer machine pump water faster than older. The only legal (by plumbing code) solution is to replace the drain piping with larger piping. Depending on where you live, this could be time-consuming and expensive. If you can find a plumber who will do it, the hose can be "hard piped", but this violates plumbing code.