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.
CITATION STYLE
Ahmad, S., & Ambrosetti, A. (2015). First order linear differential equations. In UNITEXT - La Matematica per il 3 piu 2 (Vol. 88, pp. 1–14). Springer-Verlag Italia s.r.l. https://doi.org/10.1007/978-3-319-16408-3_1
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