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View Equation

The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:1. Ordinary Differential Equations
Subcategory:1.6. Systems of Two Nonlinear Equations
Equation(s):\noindent
$\displaystyle x''_{tt}=xf(x^2+y^2,y/x)-yg(y/x)$,\hfill\break
$\displaystyle y''_{tt}=yf(x^2+y^2,y/x)+xg(y/x)$.
Solution(s),
Transformation(s),
Integral(s)
:
\noindent
Particular solution:\hfill\break
$\displaystyle u=r(t)\cos\beta,\quad \ w=r(t)\sin\beta$,\hfill\break
where the constant $\beta$ is a solution of the transcendal equation\hfill\break
$g(\tg\beta)=0$\hfill\break
and the function $r=r(t)$ is determined by the autonomous ordinary differential equation\hfill\break
$r''_{tt}=rf(r^2,\tg\beta)$.
Remarks:If $g(z)=0$, then $\beta$ is an arbitrary constant.
Novelty:New equation(s) & solution(s) / integral(s)
Author/Contributor's Details
Last name:Polyanin
First name:Andrei
Country:Russia
City:Moscow
Statistic information
Submission date:Thu 07 Dec 2006 11:28
Edits by author:0

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