Convert the following to a first order system $$x''(t) = k_x(x(t) - y(t))^{-2}, \ \ y''(t) = k_y(x(t) - y(t))^{-2},$$ $$x'(0)=v_x, \ \ y'(0) = v_y, \ \ x(0) = x_0, \ \ y(0) = y_0.$$
I know how to reduce simpler systems, by using a substitution. However, I'm lost when all of these variables are involved.