Hi everyone, I know that this system dont have analytical solutions. I want to get numerical solutions, but in function of some constants $A\_i$. Mathematica can help me, but if somebody have idea? This equations describe a physical model 


$$ A\_6 x + A\_4 (y')^2 - 2 A\_2 x'' - A\_3xy'' + A\_4yy'' = 0$$


$$ A\_5 - A\_3 (x')^2 - A\_3xx'' + A\_4yx'' - 2A\_1y'' = 0$$


$'=(d/dt)$, $''=(d^2/dt^2)$, $A\_i$-known constants. The initial conditions are:


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


Thank you in advance!!! 



system of two second order differential equations
You can reduce the number of parameters quite a bit, for starters. Set 
$$x = \alpha u , \; y = \beta v, \; t = \gamma \tau
$$  

and write $\dot w = \frac{d}{d \tau} w, \ddot w = \frac{d^2}{d\tau^2} w$. By choosing the constants $\alpha, \beta, \gamma$ properly, you should be able to nondimensionalize the system to something like
$$c u + (\dot v)^2 - \ddot u - d u \ddot v + v \ddot v = 0$$
$$1 - (\dot u)^2 - u \ddot u + d^{-1} \ddot u v - \ddot v = 0 $$
$$
u(0) = \tilde a, \; v(0) = \dot u(0) = \dot v(0) = 0.
$$
So there are only three independent constants in the system, not 7.


