Abstract
In this chapter we will consider simultaneous first order differential equations in several variables, that is, equations of the form
A solution of Equation (1) is n functions xl(t),…,xn(t) such that \( \frac{{d{x_j}\left( t \right)}}{{dx}} = {f_j}\left( {t,{x_1}\left( t \right),...,{x_n}\left( t \right)} \right),j = 1,2,...,n \) For example, xl(t) = t and x2(t) = t2 is a solution of the simultaneous first order differential equations \( \frac{{d{x_1}}}{{dt}} = 1 \) and \( \frac{{d{x_2}}}{{dt}} = 2{x_1} \) Since \( \frac{{d{x_1}^{\left( t \right)}}}{{dt}} = 1 \) and \( \frac{{d{x_2}^{\left( t \right)}}}{{dt}} = 2t = 2{x_1}\left( t \right) \) dt
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© 1975 Springer Science+Business Media New York
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Braun, M. (1975). Systems of Differential Equations. In: Differential Equations and Their Applications. Applied Mathematical Sciences, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4969-4_3
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DOI: https://doi.org/10.1007/978-1-4757-4969-4_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90114-5
Online ISBN: 978-1-4757-4969-4
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