Find an interval centered about x=0 for which the given initial value problem has a unique solution

y''+(tanx)y=e^x; y(0)=1, y'(0)=0

I know this has something to do with a_n=0 and in this case a_n=a_2=1, a_1=tanx a a_0=e^x but I am kind of confused with what the question is asking? Since a_2 does not = 0 then a unique solution would lie along any interval (-inf,inf) ? Is this correct?

Question

Find an interval centered about x=0 for which the given initial value problem has a unique solution

y''+(tanx)y=e^x; y(0)=1, y'(0)=0

I know this has something to do with a_n=0 and in this case a_n=a_2=1, a_1=tanx a a_0=e^x but I am kind of confused with what the question is asking? Since a_2 does not = 0 then a unique solution would lie along any interval (-inf,inf) ? Is this correct?