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Homework Statement
Homework Equations
Wronskian theorem:
The Attempt at a Solution
I've gotten the relationship given by the question but I do not know how to continue.
Since ##\psi_n(a)=\psi_n(b)=0##,
LHS ##=\psi_n'(b)\,\psi_{n+1}(b)-\psi_n'(a)\,\psi_{n+1}(a)##
If LHS ##=0##, RHS ##=0##, then by the First Mean Value Theorem for Integrals, ##\psi_{n+1}(c)=0## for some ##c\in(a,b)##.
But LHS is not necessarily ##0##.
Attached below is the derivation of Wronskian theorem.
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