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IMCS/Publications/BASM/Issues/BASM n.2 (42), 2003/

On initial value problem in theory of the second order differential equations. (English)

Authors: Driuma Valeriu, Maxim Pavlov.

Abstract

We consider the properties of the second order nonlinear differential equations b"= g(a,b,b') with the function g(a,b,b'=c) satisfying the following nonlinear partial differential equation: gaacc + 2cgabcc + 2ggaccc + c2gbbcc + 2cggbccc + g2gcccc + (ga+cgb)gccc - 4gabc - 4cgbbc - cgcgbcc - 3ggbcc - gcgacc + 4gcgbc - 3gbgcc + 6gbb = 0. Any equation b" = g(a,b,b') with this condition on the function g(a,b,b'}) has the General Integral F(a,b,x,y)=0 shared with General Integral of the second order ODE's y" = f(x,y,y') with the condition (d4f)/(dy'4) = 0 on the function f(x,y,y') or y" + a1(x,y)y'3 + 3a2(x,y)y'2 + 3a3(x,y)y' + a4(x,y) = 0 with some coefficients ai(x,y).

Valerii Dryuma
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str.,
Chisinau, MD-2028, Moldova
E-mail:
Maxim Pavlov
Landau ITP, RAS, Kosygina 2,
Moscow, Russia
E-mail:

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