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

Resonance ◽  
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

scholarly journals APPLICATIONS OF LIE SYSTEMS IN DISSIPATIVE MILNE–PINNEY EQUATIONS

2009 ◽  
Vol 06 (04) ◽  
pp. 683-699 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
JAVIER DE LUCAS
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Geometric Approach ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Particular Solutions ◽  
Systems Of Differential Equations ◽  
Lie Systems ◽  
Linear Differential

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.

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

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
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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