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 ON THE TRANSFORMATION OF THE LINEAR DIFFERENTIAL EQUATION INTO A SYSTEM OF THE FIRST ORDER EQUATIONS

2019 ◽  
pp. 71-75
Author(s):  
M.I. Ayzatsky
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Second Order ◽  
Dimensional System ◽  
Third Order ◽  
Order Linear ◽  
First Order ◽  
The Third ◽  
Linear Differential

The generalization of the transformation of the linear differential equation into a system of the first order equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of first order equations that can be useful for analysis of the solutions of the N-th-order differential equations. In particular, for the third-order linear equation the nonlinear second-order equation that plays the same role as the Riccati equation for second-order linear equation is obtained.

6. Laboratory Notes by Professor Tait (b) On a Mechanism for Integrating the General Linear Differential Equation of the Second Order

1878 ◽  
Vol 9 ◽  
pp. 118-120
Author(s):  
Tait
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Royal Society ◽  
Second Order ◽  
General Linear ◽  
Linear Differential

I am anxious to explain to the Society a kinematical device for the solution of the General Linear Differential Equation of the Second Order before I become acquainted with the principle of the integrating machine which, I understand, was described last Thursday by our President to the Royal Society.

THE EFFECT OF ATMOSPHERE DEPLETION IN SPHERICAL DIFFUSION FLAMES

1956 ◽  
Vol 34 (1) ◽  
pp. 54-64 ◽  
Author(s):  
R. J. Cvetanović
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Diffusion Flames ◽  
Second Order ◽  
Direct Evaluation ◽  
Exponential Solution ◽  
Non Linear ◽  
Linear Differential ◽  
Spherical Diffusion

Solutions of the second order non-linear differential equation of spherical diffusion flames have been obtained for the range of conditions of experimental interest. Deviations from the simplified exponential solution are presented in a form suitable for their direct evaluation. Some recent contributions to the theory of the method are discussed.

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