APPLICATIONS OF LIE SYSTEMS IN DISSIPATIVE MILNE–PINNEY EQUATIONS

We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express the general solution of a dissipative Milne–Pinney equation in terms of particular solutions of a system of second-order linear differential equations and a set of constants.

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An Alternative Approach to Write the General Solution of a Class of Second-order Linear Differential Equations

Resonance ◽

10.1007/s12045-021-1170-8 ◽

2021 ◽

Vol 26 (5) ◽

pp. 705-714

Author(s):

Dharm Prakash Singh ◽

Amit Ujlayan

Keyword(s):

General Solution ◽

Differential Equations ◽

Second Order ◽

Linear Differential Equations ◽

Order Linear ◽

Alternative Approach ◽

Linear Differential

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Particular Solutions of Second Order Linear Differential Equations with Constant Coefficients

Mathematics Magazine ◽

10.2307/3029047 ◽

1958 ◽

Vol 32 (1) ◽

pp. 25 ◽

Cited By ~ 1

Author(s):

C. A. Grimm

Keyword(s):

Differential Equations ◽

Second Order ◽

Linear Differential Equations ◽

Order Linear ◽

Particular Solutions ◽

Constant Coefficients ◽

Linear Differential

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A computer program to find analytical solutions of second order linear differential equations

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.1620060420 ◽

1973 ◽

Vol 6 (4) ◽

pp. 603-606

Author(s):

S. J. Farlow

Keyword(s):

Differential Equations ◽

Computer Program ◽

Analytical Solutions ◽

Second Order ◽

Linear Differential Equations ◽

Order Linear ◽

Linear Differential

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Uniform Asymptotic Solutions of a Class of Second-Order Linear Differential Equations Having a Turning Point and a Regular Singularity, with an Application to Legendre Functions

SIAM Journal on Mathematical Analysis ◽

10.1137/0517033 ◽

1986 ◽

Vol 17 (2) ◽

pp. 422-450 ◽

Cited By ~ 19

Author(s):

W. G. C. Boyd ◽

T. M. Dunster

Keyword(s):

Differential Equations ◽

Turning Point ◽

Second Order ◽

Linear Differential Equations ◽

Asymptotic Solutions ◽

Legendre Functions ◽

Regular Singularity ◽

Order Linear ◽

Linear Differential

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Second order linear differential equations with almost periodic solutions

Acta Mathematica Sinica English Series ◽

10.1007/bf02594892 ◽

1991 ◽

Vol 7 (4) ◽

pp. 354-359 ◽

Cited By ~ 6

Author(s):

Xiao Tijun ◽

Liang Jin

Keyword(s):

Differential Equations ◽

Periodic Solutions ◽

Second Order ◽

Linear Differential Equations ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Order Linear ◽

Linear Differential

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Summability criteria for oscillation of second order linear differential equations

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/bf02415185 ◽

1968 ◽

Vol 79 (1) ◽

pp. 391-398 ◽

Cited By ~ 10

Author(s):

W. J. Coles ◽

D. Willett

Keyword(s):

Differential Equations ◽

Second Order ◽

Linear Differential Equations ◽

Order Linear ◽

Linear Differential

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L p-perturbations of second order linear differential equations

Mathematische Annalen ◽

10.1007/bf01351788 ◽

1975 ◽

Vol 215 (1) ◽

pp. 23-34 ◽

Cited By ~ 4

Author(s):

Man Kam Kwong

Keyword(s):

Differential Equations ◽

Second Order ◽

Linear Differential Equations ◽

Order Linear ◽

Linear Differential

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A mechanical method for the solution of second-order linear differential equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100009804 ◽

1931 ◽

Vol 27 (4) ◽

pp. 546-552 ◽

Cited By ~ 1

Author(s):

E. C. Bullard ◽

P. B. Moon

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Boundary Conditions ◽

Order Differential Equation ◽

Second Order ◽

Linear Differential Equations ◽

Mechanical Method ◽

Order Linear ◽

Second Order Differential Equation ◽

Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

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