Abstract
A differential equation is an equation involving an unknown function and its derivatives. By a solution of a differential equation we mean a function that is differentiable and satisfies the equation on some interval. For example, x′ − x = 0 is a differential equation involving an unknown function x and its first derivative with respect to an independent variable that we may call t, s, etc. We notice that (e t)′ −e t = e t−e t = 0 for all t in the interval I = (−∞; ∞). Therefore, x(t) = e t is a solution of the differential equation on the interval I.
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© 2015 Springer International Publishing Switzerland
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Ahmad, S., Ambrosetti, A. (2015). First order linear differential equations. In: A Textbook on Ordinary Differential Equations. UNITEXT(), vol 88. Springer, Cham. https://doi.org/10.1007/978-3-319-16408-3_1
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DOI: https://doi.org/10.1007/978-3-319-16408-3_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16407-6
Online ISBN: 978-3-319-16408-3
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