Given an IVP d"y an (x) dn-1 + an-1(x)- drn-1 dy +...+ a1 (x) + ao (2)y = g(x) dx y(To) = Yo, y'(ro) = Y1, ·…, y(a-1)(xo) = Yn–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 ro e I that exists on the whole interval I Consider the IVP on the whole real line d'y - 36) d'y dy + y = sin(x) 1 (22 +x4. + dr3 2² + 36 dx y(3) = 916, y'(3) = 14, y"(3) = 8, y"(3) = 8, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval