Hi guys I have the following system and i am trying to make the appropriate substitutions to break down the system to a first order system of 4 ODE.
$$y''_1 = y_1 + 2y'_2 - \frac{y_1+\mu}{D_1} - \frac{y_1- \mu }{D_2} $$
where
$$D_1 =((y_1 +\mu^2)+y^2)^{3/2}$$ and $$D_2=((y_1-v)^2+y^2_2)^{3/2}$$
and
$$y''_2 = y_2 + 2y'_1 - v \frac{y_1+\mu}{D_1} - \mu \frac{y_1- \mu }{D_2} $$
I am a bit confused about making the substitutions can anyone help and guide as to how to get the system of 4 first order equations?