Differential Equations: Recursive Functions Functions I have some familiarity with look so, $y^\prime(x) = \tan(x+2)$: straightforward expression of the first derivative of y as a function of x.
But say I have a function, $y^\prime(x) = \cos{(y)}$?  I'm not sure what 'y' is supposed to signify when it's being called recursively like this: $y(x), \ y^\prime(x), \ $ or something else.  
If it's not saying, $y^\prime(x)= \cos{\left(\int y^\prime(x) \ \text{d}x \right)}$, what is it saying?  Any insights would be greatly appreciated...

You have: $\dfrac{dy}{dx} = \cos y \to \dfrac{dy}{\cos y} = dx \to x = \displaystyle \int \sec ydy$. Can you continue? more generally, you have a separable ODE: $y' = f(y)$, then the way to solve it is "separate" the $x$ and the $y$. like the one I did. 
