for the differential equation
t^2y''-2ty'+2y=0 with the general solutions y=C(t) + D(t^2) where C and D are constants. given the inital solution y(0)=1 and y'(0)=1 there are no solutions that exist. Why does this not contradict the Existence and Uniqueness Theorem?
The Attempt at a Solution
This theorem says that all linear, homogeneous equations have a solution. Since t^2, -2t and 2 are all continuous I don't understand why there is no solution?