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

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1 Point Given An Ivp Fundamental Existence Theorem For Linear Differential Equations D Y Dan An X Dy 1 X 1 (38.73 KiB) Viewed 13 times

(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations d" y dan an(x) dy -1(x)- +... - + 9₁ (2) de +an-1 (x² dy dan-1 y(zo) = yo, y' (zo) = 3₁,, y¹) (o) = Yn-1 If the coefficients a, (2),..., ao(x) and the right hand side of the equation g(x) are continuous on an interval I and if an(a) 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 + a(z)y= g(x) d³y 1 9) d'y dy da dr³ z²+9 dr +y=sin(x) y(1) 1979, y'(1) = 19, y"(1) = 3, y" (1) = 10, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval +