ALGEBROID SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

2019 ◽  
Vol 103 (2) ◽  
pp. 71-81
Author(s):  
Guozhen Ren
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Algebraic Differential Equations ◽  
Order Algebraic

scholarly journals The motions of algebraic differential equations

1984 ◽  
Vol 25 (1) ◽  
pp. 93-96
Author(s):  
Lee A. Rubel
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Algebraic Differential Equations ◽  
First Order ◽  
Order Algebraic ◽  
Independent Variable

We confine ourselves, for simplicity, to first-order algebraic differential equations (ADE's), although analogous considerations may be made for higher-order ADE's:P(x, y(x), y'(x)) = 0. (*)A motion of (*) is a change of independent variable that takes solutions to solutions, that is, a suitable map <p of the underlying interval I into itself so that if y is a solution of (*) then y ° φ is a solution of (*), i.e.

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