I am trying to find the fixed points of a set of coupled differential equations, which are as follows:
$y_1^\prime = y_2$, $y_2^\prime = -\sin(y_1)$
My first attempt involved integrating $y_2^\prime$, which lead to the solutions:
1. $(c,0)$
2. $(0,-c/t)$
3. $(\arcsin(c/t),-c/t)$
My second attempt involved logic, and I got the answer: $(0,n\pi)$ where $n$ is any integer.
I am unsure if either of these answers are correct, or what to do to get the correct answer. Any help would be greatly appreciated!
Hint: for $(y_1, y_2)$ to be a fixed point, you want the right sides of your system of differential equations to be $0$. No integration is needed.