On Equation for Initial Values in Theory of the Second Order Ordinary Differential Equations
| dc.creator | Dryuma, Valerii S. | |
| dc.creator | Pavlov, Maxim | |
| dc.date | 2002-07-19 | |
| dc.date.accessioned | 2026-07-07T05:34:13Z | |
| dc.date.available | 2026-07-07T05:34:13Z | |
| dc.description | 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 $$ \frac{d^2 g_{cc}}{da^2}-g_{c}\frac{dg_{cc}}{da}-4\frac{dg_{bc}}{da}+ $$ $$ +4g_{c}g_{bc}-3g_{b}g_{cc}+6g_{bb}=0, $$ where: $$ \frac{d}{da}=\frac{\partial}{\partial a}+c \frac{\partial}{\partial b}+ g \frac{\partial}{\partial c}. $$ Any equation b''=g(a,b,b') with this condition on 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 condition $\frac{\partial^4 f}{\partial y'^4}=0$ on function f(x,y,y') or $$ y''+a_{1}(x,y)y'^3+3a_{2}(x,y)y'^2+3a_{3}(x,y)y'+a_{4}(x,y)=0 $$ with some coefficients a_{i}(x,y). | |
| dc.description | 8 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/nlin/0207035 | |
| dc.identifier | http://arxiv.org/abs/nlin/0207035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80284 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 51-XX | |
| dc.title | On Equation for Initial Values in Theory of the Second Order Ordinary Differential Equations | |
| dc.type | text |