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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
##### Keywords:
Euler differential equation
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##### References:
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