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I know one more thing from physical system. If we can assume the solutions in form

$x=Ae^{jp_1t}, \quad y=Be^{jp_2t}, \quad j=\sqrt{-1}.$

I know that

$p_1=2p_2.$

If someone can help me. It is need to find a analytic or numeric solutions where $D_i$ are known constants. If the system can describe by lower number of constants and lower order, how can I get a numerical solutions in function of this constants using some of methods (perturbation or some software - Mathematica).

The equations are as follows:

$D_1x''+D_2y''(x'-y')-D_2x'y'+D_3x=0,$

$D_4y''+D_2x''(x'-y')+D_2x'y'+D_5=0.$

With the initial conditions

$x(0)=a, \quad y(0)=0, \quad x'(0)=0, \quad y'(0)=0.$

where $(')=d/dt$ and $('')=d^2/dt^2$.

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    "numeric solutions" - in *Mathematica*, you can use `NDSolve[]`; it doesn't look to me like an obviously symbolically solvable DE system...2011-05-07

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