Sturm-Liouville Separation theorem

[kidsasd987]

Hi, I wonder why wronskian must be constant.

I know that p(x)W[u1(x),u2(x)]=constant, according to the Abel's theorem, but
wouldnt there a special case that W[u1(x),u2(x)]=c/p(x).

Then for this special case, W[u1(x),u2(x)]=/=c and satisfies Abel's theorem.
Is it ok to ignore this special case?

 

[mathwonk]

this question is incomprehensible to me in connection with the accompanying text.