On general solution of a first-order non-linear differential equation of the formx(dy/dx)=y (λ+f (x, y)) with negative rational λ

1980 ◽  
Vol 126 (1) ◽  
pp. 19-80 ◽  
Author(s):  
Masahiro Iwano
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Linear Differential Equation ◽  
First Order ◽  
Non Linear ◽  
Linear Differential

scholarly journals Teknik Penentuan Solusi Sistem Persamaan Diferensial Linear Non-Homogen Orde Satu

Matematika ◽  
2019 ◽  
Vol 18 (1) ◽  
Author(s):  
Ahmad Nurul Hadi ◽  
Eddy Djauhari ◽  
Asep K Supriatna ◽  
Muhamad Deni Johansyah
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Linear Differential Equation ◽  
Homogeneous Solution ◽  
Variation Method ◽  
General Solutions ◽  
First Order ◽  
Linear Differential ◽  
Homogeneous Linear ◽  
Homogeneous Linear Differential Equation

Abstrak. Penentuan solusi sistem persamaan diferensial linear non-homogen orde satu dengan koefisien konstanta, dilakukan dengan mengubah sistem persamaan tersebut menjadi persamaan diferensial linear non homogen tunggal. Dari persamaan diferensial linear non homogen tunggal tersebut kemudian dicari solusi homogennya menggunakan akar-akar karakteristiknya, dan mencari solusi partikularnya dengan metode variasi parameter. Solusi umum dari persamaan diferensial linear tersebut adalah jumlah dari solusi homogen dan solusi partikularnya. Persamaan diferensial linear tunggal tersebut berorde- , yang solusi umumnya berbentuk . Selanjutnya dicari solusi umum berebentuk  yang berkaitan dengan , solusi umum berbentuk  yang berkaitan dengan  dan , solusi umum berbentuk  yang berkaitan dengan , , dan , demikian seterusnya sampai mencari solusi umum berbentuk  yang berkaitan dengan , , , , . Kumpulan solusi umum yang berbentuk  merupakan solusi umum dari sistem persamaan diferensial linear non homogen orde satu tersebut.Kata kunci:  Diferensial, Linear, Non-Homogen, Orde, Satu. Technical to Find The System of Linear Non-Homogen Differential Equation of First OrderAbstract. Determination of first-order non-homogeneous linear differential equation system solutions with constant coefficients, carried out by changing the system of equations into a single non-homogeneous linear differential equation. From a single non-homogeneous differential equation, a homogeneous solution is then used using its characteristic roots, and looking for a particular solution with the parameter variation method. The general solution of these linear differential equations is the number of homogeneous solutions and their particular solutions. The single linear differential equation is n-order, the solution being in the form of  . Then look for a general solution in the form of  related to , a general solution in the form of related to  and , general solutions in the form of related to  ,  and , and so on until looking for a general solution in the form of  related to , , ,  ..., . A collection of general solutions in the form of , , , ...,  is the general solution of the first-order non-homogeneous linear differential equation system.Keywords: Linear, Differential, First, Order, Non-Homogeneous

4. On the Linear Differential Equation of the Second Order

1878 ◽  
Vol 9 ◽  
pp. 93-98 ◽  
Author(s):  
Tait
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Arbitrary Constant ◽  
Second Order ◽  
General Linear ◽  
First Order ◽  
Non Linear Equation ◽  
Non Linear ◽  
Linear Differential

This paper contains the substance of investigations made for the most part many years ago, but recalled to me during last summer by a question started by Sir W. Thomson, connected with Laplace's theory of the tides.A comparison is instituted between the results of various processes employed to reduce the general linear differential equation of the second order to a non-linear equation of the first order. The relation between these equations seems to be most easily shown by the following obvious process, which I lit upon while seeking to integrate the reduced equation by finding how the arbitrary constant ought to be involved in its integral.

Design and Analysis of an oil Cushion

1973 ◽  
Vol 15 (1) ◽  
pp. 48-52 ◽  
Author(s):  
M. A. Satter
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Dynamic Characteristics ◽  
Order Linear Differential Equation ◽  
First Order ◽  
Non Linear Equation ◽  
Non Linear ◽  
Linear Differential ◽  
Good Agreement

The dynamic characteristics of an oil cushion, which was originally designed to eliminate impactive excitation to a mechanical lever and thereby achieve noise reduction, have been studied both theoretically and experimentally. The system motion is represented by a second order non-linear differential equation which can be reduced to a first order linear differential equation by changing the variables. An approximate but simple solution to the non-linear equation has also been presented. Theoretical and experimental results have good agreement.

scholarly journals Steady Motion of Ice Sheets

1980 ◽  
Vol 25 (92) ◽  
pp. 229-246 ◽  
Author(s):  
L. W. Morland ◽  
I. R. Johnson
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Power Law ◽  
Perturbation Expansion ◽  
Ice Sheet ◽  
Leading Order ◽  
Plane Flow ◽  
General Law ◽  
Non Linear ◽  
Linear Differential

AbstractSteady plane flow under gravity of a symmetric ice sheet resting on a horizontal rigid bed, subject to surface accumulation and ablation, basal drainage, and basal sliding according to a shear-traction-velocity power law, is treated. The surface accumulation is taken to depend on height, and the drainage and sliding coefficient also depend on the height of overlying ice. The ice is described as a general non-linearly viscous incompressible fluid, with illustrations presented for Glen’s power law, the polynomial law of Colbeck and Evans, and a Newtonian fluid. Uniform temperature is assumed so that effects of a realistic temperature distribution on the ice response are not taken into account. In dimensionless variables a small paramter ν occurs, but the ν = 0 solution corresponds to an unbounded sheet of uniform depth. To obtain a bounded sheet, a horizontal coordinate scaling by a small factor ε(ν) is required, so that the aspect ratio ε of a steady ice sheet is determined by the ice properties, accumulation magnitude, and the magnitude of the central thickness. A perturbation expansion in ε gives simple leading-order terms for the stress and velocity components, and generates a first order non-linear differential equation for the free-surface slope, which is then integrated to determine the profile. The non-linear differential equation can be solved explicitly for a linear sliding law in the Newtonian case. For the general law it is shown that the leading-order approximation is valid both at the margin and in the central zone provided that the power and coefficient in the sliding law satisfy certain restrictions.

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