- #1

- 435

- 13

## Homework Statement

Assume that y

_{1}and y

_{2}are solutions of y'' + p(t)y' + q(t)y = 0 on an open interval I on which p,q are continuous. Assume also that y

_{1}and y

_{2}have a common point of inflection t

_{0}in I. Prove that y

_{1},y

_{2}cannot be a fundamental set of solutions unless p(t

_{0}) = q(t

_{0}) = 0.

## The Attempt at a Solution

I figured that if p(t

_{0}) is not 0 or q(t

_{0}) is not 0 then its not a fundamental set of solutions. So I have to show for the three cases

i) p(t

_{0}) =/= 0 q(t

_{0}) = 0

ii) p(t

_{0}) = 0 q(t

_{0}) =/= 0

ii) p(t

_{0}) =/= 0 q(t

_{0}) =/= 0

That the Wronskian is 0, but I don't know what to do to relate p to q in the wronskian.