(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations d" y an (x)- dan +an-1(x)= du-ly

[answerhappygod]

1 Point Given An Ivp Fundamental Existence Theorem For Linear Differential Equations D Y An X Dan An 1 X Du Ly 1 (39.53 KiB) Viewed 13 times

(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations d" y an (x)- dan +an-1(x)= du-ly dan-1 d²y da2 y(zo) yo, y' (ro) = ₁,., y(n-1) (20)=Yn-1 If the coefficients a, (a),..., ao (a) and the right hand side of the equation g(x) are continuous on an interval I and if an (r) 0 on I then the IVP has a unique solution for the point o I that exists on the whole interval I. Consider the IVP on the whole real line sin(2) dy + a₁(x)- + ao(x)y= g(x) da + cos(z) da dy + sin(a)y=tan(a) y(0.5)= 3, y'(0.5) = 7, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval