I have given the following 2nd order DE:
$ \ddot{q_1} = - \frac{q_1}{|q|^3} $ $ \ddot{q_2} = - \frac{q_2}{|q|^3} $ with $|q| = \sqrt{q_1^2 + q_2^2}$
The assignment is to solve this using explicit and implizit Euler. As for the explicit, I could split this into a system of 1st order DEs using $\dot{q} = p$, thus I had $ \dot{p_1} = - \frac{q_1}{|q|^3} $ $ \dot{p_2} = - \frac{q_2}{|q|^3} $ $ \dot{q} = p $
But now I am stuck at the implicit Euler. The reason is: The equation for this is $\dot{y}_{n+1} = y_n + \Delta t f(y_{n+1})$.
My problem now is: I do not have all q or all p in my function f, but $\dot{p} = f(q)$ So how can I formulate this method?