I know one more thing from physical system. If we can assume the solutions in form $$x=Ae^{jp_1t}, \quad y=Be^{jp_2t}, \quad j=-1^{1/2}$$ 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)

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

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

Initial conditions

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

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

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