determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation t²z'' 2tz'=cost, given that z(0)=6 and z'(0)=9. If a conclusion can be drawn, discuss it If a conclusion cannot be drawn, explain why.

Select the correct choice below and fill in any answer boxes to complete your choice.

A A solution is guaranteed on the interval __B. No conclusion can be drawn because the functions p(t) = ___, q(t)= ___, and g(t)=___ are not simultaneously continous of any interval that contains the point t0 = __
C. A solution is guaranteed only at the point t0 = __ because the functions p(t)=__, g(t)=__ , and g(t)=___ are simultaneously defined at that point
D. No conclusion can be drawn because the conditions z(0)= 5 and z,(0)=9 do not provide enough information to determine all constants of integration.