(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations d" y an(x) dan + an-1(2). dn 1 da

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1 Point Given An Ivp Fundamental Existence Theorem For Linear Differential Equations D Y An X Dan An 1 2 Dn 1 Da 1 (41.71 KiB) Viewed 14 times

(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations d" y an(x) dan + an-1(2). dn 1 da"-1 = y(zo) 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(x)0 on I then the IVP has a unique solution for the point zo € I that exists on the whole interval I. Consider the IVP on the whole real line y0, y' (ro) = y₁, ..., y(¹)(xo) - Yn-1 = dy +...+(2). + ao(x)y= g(x) da + (²+36)- da y(-14) 44, y'(-14) = 13, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval dr³ + 1 dy +y=sin(x) (x²-36) da "(-14) = 3, "(-14) - 9,