On initial value problem in theory of the second order differential equations
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DRYUMA, Valery, PAVLOV, Maxim. On initial value problem in theory of the second order differential equations. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, nr. 2(42), pp. 51-58. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(42) / 2003 / ISSN 1024-7696 /ISSNe 2587-4322

On initial value problem in theory of the second order differential equations

Pag. 51-58

Dryuma Valery, Pavlov Maxim
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 17 decembrie 2013


Rezumat

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 @4f @y′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).

Cuvinte-cheie
dual equation, space of linear elements, projective connec- tion.