Approximately n-order linear differential equations

We prove the generalized Hyers--Ulam stability  of n-th order linear differential equation of the form y^{(n)}+p_{۱}(x)y^{(n-۱)}+ \cdots+p_{n-۱}(x)y^{\prime}+p_{n}(x)y=f(x), with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Keywords:

Hyers-Ulam stability , Linear differential equation , homogeneous equation