Literally do not know where to start on this one. I've only learnt Multiplicative separation but I think I might be over thinking it.
I've uploaded a capture below
Assuming that is a constant, you have and if we let , since the first term is only a function of and the second is only a function of , then evaluating derivatives gives and , and substituting gives
Since the left hand side is only a function of and the right hand side is only a function of , the only way they can be equal is if they are both equal to some constant value . This gives
which are two ordinary differential equations