Lowest order equation for zeros of a homogeneous linear differential polynomial

A method for solving first order fuzzy differential equation

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y = λ0(x)y ′ + s0(x)y, where λ0(x), s0(x) are C −functions. We prove (i) if the differential equation, has a polynomial solution of degree n > 0, then δn = λnsn−1 − λn−1sn = 0, where λn = λ ′ n−1 + sn−1 + λ0λn−1 and sn = s ′ n−1 + s0λk−1, n = 1, 2, . . . . Conversely (ii) if λnλn−1 6= 0 and δn = 0, then the differential equation has a polynomial solution o...

Constructing a Third-Order Linear Differential Equation

In this paper, using the approach of Hurwitz and the necessary conditions given in 4,6], we construct a third order linear diierential equation whose diierential Galois group is the primitive subgroup F SL3 36 S L(3; C) of order 108.

General Solution for Fuzzy Linear Second Order Differential Equation Using First Solution

The fuzzy linear second order equations with fuzzy initial values are investigatedin this paper. The analytic general solution solutions of them usinga rst solution is founded. The parametric form of fuzzy numbers is appliedto solve the second order equations. General solutions for fuzzy linear secondorder equations with fuzzy initial values are investigated and formulatedin four cases. A examp...

An Algorithm for Solving Second Order Linear Homogeneous Differential Equations

In th is paper we present an algor i thm for f inding a "c losed-form" solut ion of the dil l-erential equatiofl -1"'+ ql +by, where a and b are rational functions of a complex var iable .x. provided a "c losed-form" solut ion exists. The algor i thm is so arranged that i f no solut icrn is found. then no solut ion can exist . The frrst sect ion makes precise what is meant by "c losed-form" and...