It has been a very long time since I have worked with differential equations.
I have $y' = -y^2$ and $y(0) = 1$ and I want to solve this with RK$3$. I know the iterative formula for RK$3$, but I am not sure how to get this going with this 'odd' form of $y' = -y^2$. I'm used to getting something as $f(t_n,x_n)$.
$$ x_{n+1} = x_{n} + h \left( \frac{1}{6}k_1 + \frac{2}{3}k_2 + \frac{1}{6}k_3 \right) $$
How do I get this going?
Thank you.