Given An Ivp Fundamental Existence Theorem For Linear Differential Equations D Y Dx D Ly Y An 1 X Dxn 1 A X D 1 (33.3 KiB) Viewed 51 times
Given An Ivp Fundamental Existence Theorem For Linear Differential Equations D Y Dx D Ly Y An 1 X Dxn 1 A X D 2 (8.88 KiB) Viewed 51 times
Given an IVP Fundamental Existence Theorem for Linear Differential Equations d" y dx" d-ly 'y +an-1(x)- dxn-1 + a₁ (x) dy dx y(xo) = = yo, y' (xo) = y₁, ..., y(n-¹)(x) = Yn-1 d³y dx³ y(-21) = -80, y(-21) = 6, (x² + 121) + If the coefficients a, (x), ..., ao (x) and the right hand side of the equation g(x) are continuous on an interval I and if a,, (x) #0 on I then the IVP has a unique solution for the point xo EI that exists on the whole interval I. Consider the IVP on the whole real line d'y dx4 + +4 ... + + ao(x) y = g(x) 1 dy (x² - 121) dx y'(-21) = 2, "(-21) = 6, + y = sin(x)
The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval
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