Show that the second-order differential equation y = F(x, y, y) can be reduced to a system

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Show that the second-order differential equation y″ = F(x, y, y′) can be reduced to a system of two first-order differential equations

Can something similar be done to the nth-order differential equation y⁽ⁿ⁾ = F(x, y, y′, y″,c, y^(n-1))?

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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Question Posted: May 02, 2023 02:50 AM

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Show that the second-order differential equation y = F(x, y, y) can be reduced to a system

Question:

dy dx dz dx Z, = F(x, y, z).

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Thomas Calculus Early Transcendentals

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