answer given
(a) y(t) =
c0(1-t2+1/3t4+......) +
c1(t-1/2t3+1/8t5 + ......)
(b) y(t) = 3(1-t2+1/3t4+....)
-2(t-1/2t3+1/8t5 + ...)
The initial-value problem, y" + ty + 2y = 0, y(0) = 3, y'(0) = -2, [infinity] has a power series solution of the form y(t) = Σcnt" that is guaranteed to be absolutely convergent in the interval |t|