approximately n-order linear differential equations

Approximately $n$-order linear differential equations

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ 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.

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Irreducible Linear Differential Equations of Prime Order

With the exception of a nite set of nite diierential Galois groups, if an irreducible linear diierential equation L(y) = 0 of prime order with unimodular diierential Galois group has a Liouvillian solution, then all algebraic solutions of smallest degree of the associated Riccati equation are solutions of a unique minimal polynomial. If the coeecients of L(y) = 0 are in Q()(x) Q(x) this unique ...

Second Order Linear and Nonlinear Differential Equations'

HIGHER-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS II: Nonhomogeneous Equations

Because the presentation of this material in class will differ from that in the book, I felt that notes that closely follow the class presentation might be appreciated.

A new approach for solving the first-order linear matrix differential equations

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...