ON THE INTEGRATING FACTORS OF THE DIFFERENTIAL EQUATION Mdx + Ndy = 0

Author(s):  
George Boole
2021 ◽  
Author(s):  
Rajnish Kumar Jha

In this paper we present a solution expression for the general Nth-order linear ordinary differential equation as our main result which involves the use of Integrating Factors where the Integrating Factors are determined using a set of equations such that when this set of equations can be solved, the solution of the concerned differential equation can be determined completely. In this regard we also present result for a special case corresponding to the main result where the solution of the general Nth-order linear ordinary differential equation can be determined completely when N-1 out of N complementary solutions are known.


1958 ◽  
Vol 25 (1) ◽  
pp. 75-78
Author(s):  
T. H. Lin

Abstract A method of calculating the creep deflections and stresses of a beam-column is shown. The differential equation of equilibrium in terms of creep strain is solved by the method of integrating factors with Green’s function. For restrained and built-in ends, the end moments are found from the end conditions. An illustrative example is given for a beam-column of an ideal H-section with built-in ends and subjected to uniform lateral load. The deflection-time curve and flange stresses at different instants are shown.


2020 ◽  
Vol 10 (4) ◽  
pp. 143-152
Author(s):  
F. Martínez ◽  

Recently exact fractional differential equations have been introduced, using the conformable fractional derivative. In this paper, we propose and prove some new results on the integrating factor. We introduce a conformable version of several classical special cases for which the integrating factor can be determined. Specifically, the cases we will consider are where there is an integrating factor that is a function of only x, or a function of only y, or a simple formula of x and y. In addition, using the Conformable Euler's Theorem on homogeneous functions, an integration factor for the conformable homogeneous differential equations is established. Finally, the above results apply in some interesting examples.


1943 ◽  
Vol 27 (276) ◽  
pp. 159-165
Author(s):  
H. Wallis Chapman

A Well-Known method of integrating the simple differential equation of the second order y″ + k 2 y = 0 .....1.1 consists in multiplying by an integrating factor 2y′ and integrating directly, when we obtain y′2 + k 2 y 2 = k 2 a 2, .....1.2 where a is an arbitrary constant.


Author(s):  
Xin Zhao ◽  
Yanxia Hu

The generalized Weierstrass integrability of a class of second-order nonlinear differential equations is considered. The conditions of existence and the corresponding expressions of generalized Weierstrass inverse integrating factors of the second-order nonlinear differential equation are presented. The relationship between the generalized Weierstrass inverse integrating factors and the Weierstrass inverse integrating factors is given. Finally, as an application of the main results, a Kudryashov-Sinelshchikov equation for obtaining traveling wave solutions is considered.


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