Abstract
In this chapter we will consider simultaneous first-order differential equations in several variables, that is, equations of the form
A solution of (1) is n functions x 1(t),..., x n(t) such that dx j(t)/dt = f j(t, x 1(t),..., x n(t)), j = 1,2,..., n. For example, x 1(t) = t and x 2(t) = t 2 is a solution of the simultaneous first-order differential equations
since dx 1(t)/dt = 1 and dx 2(t)/dt = 2t = 2x 1(t).
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© 1993 Springer Science+Business Media New York
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Braun, M. (1993). Systems of differential equations. In: Differential Equations and Their Applications. Texts in Applied Mathematics, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4360-1_3
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DOI: https://doi.org/10.1007/978-1-4612-4360-1_3
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