Going through some notes on ODE's, I came across this which I am trying to understand intuitively.
Let $y(t)$ be the solution of \begin{equation} \frac{dy(t)}{dt} = f(y(t),t). \end{equation}
Now the solution of an ODE I understand to be any function that is at least $n$ times differentiable where $n$ is the highest order term in the ODE.
I don't quite understand what the above statement is saying, is the ODE the derivative (LHS) and $y(t)$ is differentiable at least once?
The ODE is the whole equation, the highest order is one so you are correct that we require $y$ to be differentiable at least once.