I am given an ODE $$-y''(x) + q(x) y'(x) = \lambda y(x),$$
and let $y_1,y_2$ be two solutions to this ODE on $[a,b]$ to two different values $\lambda_1 \neq \lambda_2$(on the right side of this equation)
Now, suppose that there is a minimal $x \in [a,b]$ such that $W(y_1,y_2)(x)=0,$ (so for all $[a,x)$ this Wronskian is NOT zero) then I am supposed to show that also $W'(y_1,y_2)(x)=0$.
Does anybody have an idea how this could be done?
Actually, I am not sure if we really need all these requirements, but they are everything I have.