Is it possible to pass a PHD without full understanding of ones own thesis?
Of course, it would be good if someone around you can help you see what needs to be done to legitimize your use of "the other 5 equations". If you post to MathStackExchange, someone might be able to help, for example, if no one physically nearby can.

In any case, honesty and at least a nominal "dispassion" about things is the best approach, I think. Say what you assume, say what you can verify, say what previous sources say, etc. It's ok, I think, if your results are "relative" (=relative to assuming that certain sources are ok, plus assuming that certain extensions, which you've tried but failed (so far) to validate yourself first-hand, are ok...), as long as you are very clear on what your results are relative to.

Don't bluff... :)