You can use Picard's existence theorem about (a,b)=(0,12).

However, let's use brute force.

We see from the differential equation that y has derivatives of all orders. So we can calculate and express the solution in terms of a Taylor expansion:

As is well known, this converges in the neighbourhood of zero, where

Ps. There is a delicate point involving whether the Taylor series will converge to y. Since y is expressed in terms of the values of the analytic functions sin and cos, there is no problem there.