Came across this in a physics problem. Let $x$ be a plane vector dependent on time $t$. Let $\ddot{x}$ be the second order derivative of $x$ against $t$. Let $|x|$ be the Euclidean norm of vector $x$ Solve
$\ddot{x} = -a \frac{x}{|x|^3}$
I'm trying to start by solving this as an ordinary differential equation $y^{''} = -a \frac{y}{|y|^3}$ where $y$ is a scalar. But even this ODE is quite difficult to handle, especially the $|y|$ part.