1. The problem statement, all variables and given/known data Assume that y1 and y2 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 y1 and y2 have a common point of inflection t0 in I. Prove that y1,y2 cannot be a fundamental set of solutions unless p(t0) = q(t0) = 0. 3. The attempt at a solution I figured that if p(t0) is not 0 or q(t0) is not 0 then its not a fundamental set of solutions. So I have to show for the three cases i) p(t0) =/= 0 q(t0) = 0 ii) p(t0) = 0 q(t0) =/= 0 ii) p(t0) =/= 0 q(t0) =/= 0 That the Wronskian is 0, but I don't know what to do to relate p to q in the wronskian.