Given An Ivp Fundamental Existence Theorem For Linear Differential Equations An 1 X Dxn 1 Dx A X Dy N Xo 1 (30.83 KiB) Viewed 45 times
Given An Ivp Fundamental Existence Theorem For Linear Differential Equations An 1 X Dxn 1 Dx A X Dy N Xo 2 (21.06 KiB) Viewed 45 times
Given an IVP Fundamental Existence Theorem for Linear Differential Equations +an-1(x). dxn-1 dx + a₁ (x) dy (n-¹)(xo) = Yn-1 y(xo) = yo, y(xo) = y₁, 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 dx² d" y an (x)- dxn sin(x)- + ... **** + ao(x) y = g(x) dy + cos(x)- + sin(x)y=tan(x) dx y(1.25) 19, y(1.25) = 6, =
The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval
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