What is the $f(t,y)$ in this question?

Question

Euler's method requires $f(t,y)$. What's the $f(t,y)$ function in this assignment? $q(t)$ and $p(t)$ are vectors. How am I supposed to apply them in Euler's method?

Answer 1

Your unknown functions are $q_1,q_2,p_1,p_2$ the text already gives you a system of differential equations for these functions \begin{align} \dot{q}_1(t) &= p_1(t)\\ \dot{q}_2(t) &= p_2(t) \\ \dot{p}_1(t) &=\frac{-1}{\big(q_1(t)^2 + q_2(t)^2\big)^\frac{3}{2}} q_1(t) \\ \dot{p}_2(t) &= \frac{-1}{\big(q_1(t)^2 + q_2(t)^2\big)^\frac{3}{2}} q_1(t) \end{align} So your $y(t)$ is $\left[\begin{smallmatrix} q_1(t) \\ q_2(t) \\ p_1(t) \\ p_2(t) \end{smallmatrix}\right]$ and $f(t,y)$ is given by the right hand side of the differential equation.