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Hyers-Ulam stability of linear differential equations of first order. (English) Zbl 1159.34041
The authors prove the so called Hyers-Ulam stability of the linear differential equation
$p(x)y'-q(x)y-r(x)=0\tag{$$*$$}$ in the sense that there is a certain $$K>0$$ such that, if for some $$\varepsilon>0$$ and $$y\in C^1((\alpha,\beta))$$ it holds $$| p(x)y'-q(x)y-r(x)| \leq \varepsilon$$, then there is a solution $$z$$ of $$(*)$$ such that $$| y(x)-z(x)| \leq K\varepsilon.$$

##### MSC:
 34D99 Stability theory for ordinary differential equations 34A40 Differential inequalities involving functions of a single real variable
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##### References:
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