Given an nth order DE, how (intuitively and/or mathematically) does computing the Wronskian to be nonzero for at least one point in the defined interval for the solution to the DE ensure the solution is unique and also a fundamental set of solutions? Also, is it true that if W = 0, it is 0 for all entries, and also if W does not equal 0, it is never equal to 0? If so, is there a formal proof (and/or intuitive explanation) for this? Also, for a non-homogeneous DE, the solution is in the form Yhomog + Ypart = y, where Ypart is a solution to the g(t). Does Ypart necessarily have to have ALL solutions or just one?