scholarly journals A remark on the growth of solutions of first order algebraic differential equations

1980 ◽  
Vol 78 (4) ◽  
pp. 509-509 ◽  
Author(s):  
Sh. Strelitz
Keyword(s):  
Differential Equations ◽  
Algebraic Differential Equations ◽  
First Order ◽  
Order Algebraic ◽  
Growth Of Solutions

scholarly journals On the Growth of Solutions of Algebraic Differential Equations Whose Coefficients are Arbitrary Entire Functions

1970 ◽  
Vol 39 ◽  
pp. 107-117 ◽  
Author(s):  
Steven Bank
Keyword(s):  
Differential Equations ◽  
Entire Functions ◽  
Algebraic Differential Equations ◽  
First Order ◽  
Rate Of Growth ◽  
Growth Of Entire Functions ◽  
Order Algebraic ◽  
Growth Of Solutions

In this paper we treat the problem of determining the rate of growth of entire functions which are solutions of first order algebraic differential equations whose coefficients are arbitrary entire functions (i.e. equations of the form Ω(z, y, dy/dz) = 0, where Ω(z, y, dy/dz) = is a polynomial in y and dy/dz, whose coefficients fkJ(z) are entire functions).

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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