An approximation property of exponential functions
Using the power series method, the author gives a solution of the linear differential equation \[ y'(x)- \lambda y(x)= \sum_{n=0}^{\infty}a_n(x-c)^n, \] where \(y\) is a function from the real interval \((c-\rho, c+\rho)\) into the set of complex numbers, where \(\rho\) is the radius of convergence of the series on the right hand side of the equation and \(\lambda\) is a complex number. Moreover, in appropriate class of analytic functions, the author investigates the stability in Hyers-Ulam's sence of the equation \(y'(x) - \lambda y(x)=0.\)
linear first order differential equation
scientific article; zbMATH DE number 5652041