For the equation y" +p(t)y' + g(t)y = 0, assume that p. q are continuous functions, and that y and 3/2 are solutions to the ODE in an open interval I. Prove that if y and y2 have a common inflection point to E I, then they cannot form a fundamental set of solutions on I unless both p(to) and q(to) are zero. (Hint: If y(to) = 0, it implies p(to)yi (to)+q(to) (to) = 0. Similar things can be said for y/2 at to. Carefully look at this system of equations.)