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Hyers-Ulam stability of linear differential equations of first order. III. (English) Zbl 1087.34534
Summary: Let \(X\) be a complex Banach space and let \(I=(a,b)\) be an open interval. In this paper, we prove the generalized Hyers-Ulam stability of the differential equation \(ty'(t)+\alpha y(t)+\beta t^rx_0=0\) for the class of continuously differentiable functions \(f:I\to X\), where \(\alpha, \beta\) and \(r\) are complex constants and \(x_0\) is an element of \(X\). By applying this result, we also prove the Hyers-Ulam stability of the Euler differential equation of second order.

MSC:
34G10 Linear differential equations in abstract spaces
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