(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations dy an(x)- dz + an-1 dn-1 y da"-1

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1 Point Given An Ivp Fundamental Existence Theorem For Linear Differential Equations Dy An X Dz An 1 Dn 1 Y Da 1 1 (40.63 KiB) Viewed 12 times

(1 point) Given an IVP Fundamental Existence Theorem for Linear Differential Equations dy an(x)- dz + an-1 dn-1 y da"-1 -1(x). +... y(zo) yo, y' (zo) = y₁, = y(n-1) (ro)=Yn-1 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(a)0 on I then the IVP has a unique solution for the point o EI that exists on the whole interval I. Consider the IVP on the whole real line +2¹² dy • + α₁ (2). + a(z)y= g(x) da d³y da³ , 1 dy (2²-144) da +y=sin(a) ²+144 da y(14) 99, y'(14) = 12, y"(14)=6, y"(14) = 6, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval