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