I am given the differential equation $y'' + y/|y|^3 = 0$ with $y(0) = (1,0)$ and $y'(0) = (0,0.25)$. I need to convert this second order ODE into a system of first order ODEs.
So I set $y_1 = y$ and $y_2 = y' \implies y_{1}^{'} = y_2$. Then, $y_{2}^{'} = y^{''} = -y/|y|^3 = -y_1/|y_1|^3$. Since $y_1(0) = (1,0) \text{and} y_2(0) = (0,0.25)$ but then the vectors trip me up in getting the final system $(y_{1}^{'} = y_2, y_2 = " ")$. How do I deal with the vector here?