Irreducible Linear Differential Equations of Prime Order
نویسندگان
چکیده
منابع مشابه
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 ...
متن کاملApproximately $n$-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.
متن کاملOn 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
متن کاملapproximately 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.
متن کاملAn algorithm to compute Liouvillian solutions of prime order linear difference-differential equations
A normal form is given for integrable linear difference-differential equations {σ(Y ) = AY, δ(Y ) = BY }, which is irreducible over C(x, t) and solvable in terms of liouvillian solutions. We refine this normal form and devise an algorithm to compute all liouvillian solutions of such kind of systems of prime order.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1994
ISSN: 0747-7171
DOI: 10.1006/jsco.1994.1055