What is the type of singular point for £(z)= e ²

Given an IVP d"y + an-1(x) dn-ly dy +...+ a1 (x) dx + ao (x)y = g(x) drr-1 у (хо) — Уо, у (tо) — Ул, -.., у" "(2о) — Ул-1 If the coefficients an (x), ..., ao (x) and the right hand side of the equation g(x) are continuous on an interval I and if an (x) +0 on I then the IVP has a unique solution for the point xo e I that exists on the whole interval I. Consider the IVP on the whole real line d'y - 36) dx4 dy + y= sin(x) 1 (x² dz3 x2 + 36 dx у(3) — 916, у (3) — 14, у"(3) — 8, у" (3) — 8, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval

-18e5t y" – 10y/ + 25y = t² +1 Yp ||