The Monge equation and topology of solutions of the second order ODE’s
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2020-08-31 21:28
SM ISO690:2012
DRYUMA, Valery. The Monge equation and topology of solutions of the second order ODE’s. In: Conference of Mathematical Society of the Republic of Moldova. 3, 19-23 august 2014, Chișinău. Chișinău: "VALINEX" SRL, 2014, pp. 191-194. ISBN 978-9975-68-244-2.
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Conference of Mathematical Society of the Republic of Moldova
3, 2014
Conferința "Conference of Mathematical Society of the Republic of Moldova"
Chișinău, Moldova, 19-23 august 2014

The Monge equation and topology of solutions of the second order ODE’s

Pag. 191-194

Dryuma Valery
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 9 octombrie 2017


Rezumat

Properties of the Monge equation © ³ x; y; z; dy dx ; dz dx ´ = 0 associated with the partial di®erential of equation Fxx_ Fyy_ = 0 to the first integral F(x; y) = C of the system ODE x_ = P(x; y); y_ = Q(x; y) are studied. Examples of solutions of the equation P¹x Q¹y (Px Qy)¹ = 0 to the integrating multiplier ¹ = ¹(x; y) of the first order ODE Qdx¡Pdy = 0, where Q(x; y) and P(x; y) are the polynomial on x; y, are constructed. Topological properties of the relations F(x; y; a; b) = 0 which generate dual second order ODE's y00 = f(x; y; y0) and b00 = Á(a; b; b0) are considered.

Cuvinte-cheie
The Monge equation, integrating multiplier, ODE,

duality