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

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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 1 (54.34 KiB) Viewed 56 times

(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations dy +...+ a₁(x) + ao(x)y = g(x) -1) (xo) dx =Yn-1 y(xo) = yo, y' (xo) = y₁, If the coefficients an(x),..., a (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 an(x). dny dxn dn-1, ¹-¹y dxn-1 + an_1(x). ³y dx³ d³ d¹y (x² + 100) + dx4 y(−19) = 1, y'(-19) = 7, y"(−19) = 8, y"(−19) = 8, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval 1 dy (x² 100) dx + +y=sin(x)