I am given the following in order to expand a taylor series:
$$y''=3+x-y^2$$ $$y(0)=1$$ $$y'(0)= -2$$
What would the result of differentiating the first function be? I am not sure what to do with the $y$?
Does it become, $$y'''= 1 + (y')^2$$ Or would we be using partial differentials?
It is $$y'''=1-2yy'$$ by the chain rule.