(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations dy + ... + a₁(x). + ao(x)y = g(x)

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1 Point Given An Ivp Fundamental Existence Theorem For Linear Differential Equations Dy A X Ao X Y G X 1 (56.36 KiB) Viewed 37 times

(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations dy + ... + a₁(x). + ao(x)y = g(x) ,,(n-1) (xo) dx =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 o I that exists on the whole interval I. Consider the IVP on the whole real line dny dxn + an-1(x) y(xo) = yo, y' (xo) = y₁, ... y' d¹y dx4 dn-ly dxn-1 (x² – 9)- d³, dx³ + = 1 dy x² + 9 dx + y = sin(x) y(2) = 1136, y' (2) 12, y" (2) 8, y"" (2) = 5, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval