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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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