(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations an(x) dny dxn + an-1(x) dn-1₂ dxn

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1 Point Given An Ivp Fundamental Existence Theorem For Linear Differential Equations An X Dny Dxn An 1 X Dn 1 Dxn 1 (52.98 KiB) Viewed 31 times

(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations an(x) dny dxn + an-1(x) dn-1₂ dxn-1 dy +...+ a₁(x) + ao(x)y= g(x) dx y(xo): = yo, y' (xo) = y₁, y(n-1)(x) = 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 + y = sin(x) (x² 144) day +24d³y 1 dy x² + 144 dx dx4 y(15) ) = −23, y′(15) = 19, dx³ The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval y″(15) = 3, y″(15) = 3,