Systems of First Order Linear Differential Equations
Make the substitutions: x 1 = y, x 2 = y′, x 3 = y″, … , x n = y (n−1), and x n′ = y (n). The first n − 1 equations follow thusly. Lastly, substitute the x’s into the original equation to rewrite it into the n-th equation and obtain the system of the form: x 1′ = x 2 x 2′ = x 3 x 3′ = x 4 : : : : : : x n−1′ = x n n n n n ................
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