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# 11.2a - 11.2 Higher Order ODEs Transforming into a system...

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9/15/2011 1 11.2 Higher Order ODEs Transforming into a system of 1 st order ODEs Higher Order Reviewed Here’s an ? th order ODE (with I.V.s) Set Then, we obtain a system of Odes of the 1 st order:

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9/15/2011 2 Or, in Vector Notation We can write the previous system Remark: we can also introduce ? 0 𝑡 = 𝑡 to change the above into an autonomous system 𝑋 = 𝐹 𝑋 ??𝑟 𝑡 ∈ [?, ?] 𝑋 ? = 𝑆, ?𝑖𝑣?? Example: Transform a High Order ODE I.V.P: Let The system becomes
9/15/2011 3 Example: Transform a System of ODEs of High Order to a System of 1 st Order Consider a system of order 2:

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