A Non-Linear Differential Equation of the Second Order with Periodic Solutions whose Associated Limit Cycles are Algebraic Curves

1953 ◽  
Vol s1-28 (3) ◽  
pp. 356-360 ◽  
Author(s):  
Chike Obi
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Periodic Solutions ◽  
Limit Cycles ◽  
Algebraic Curves ◽  
Second Order ◽  
Non Linear ◽  
Linear Differential

Periodic solutions of a linear differential equation of the second order with periodic coefficients

1926 ◽  
Vol 23 (1) ◽  
pp. 44-46 ◽  
Author(s):  
E. L. Ince
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Periodic Solutions ◽  
Second Order ◽  
Hill’S Equation ◽  
Periodic Coefficients ◽  
Hill's Equation ◽  
Linear Differential ◽  
Image Position

The equation to be considered is of the typewhere p (x) is continuous for all real values of x, even, and periodic. It is no restriction to suppose that the period is π, and this assumption will be made, so that the equation is virtually Hill's equation.

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.

scholarly journals Existence of limit cycles for a class of autonomous systems

1983 ◽  
Vol 28 (3) ◽  
pp. 331-337
Author(s):  
Anthony Sofo
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Autonomous Systems ◽  
Non Linear ◽  
Stable Periodic ◽  
Linear Differential ◽  
Image Position

A proof is given for the existence of at least one stable periodic limit cycle solution for the polynomial non-linear differential equation of the formin some cases where the Levinson-Smith criteria are not directly applicable.

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.

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