I have the following definition of Linear Differential Equation:
A linear differential equation is any differential equation that can be written in the following form.
The important thing to note about linear differential equations is that there are no products of the function, $y(t)$, and its derivatives and neither the function or its derivatives occur to any power other than the first power.
But then I see this one:
And it's a non-linear differential equation because the function $y(t)$ is evaluated by sine which is a non-linear function (I think that's the reason, correct me if I'm wrong).
So, is this true: a differential equation is non-linear if there are (in the equation) products of the function $y(t)$ and its derivatives or, $y(t)$ or its derivatives are evaluated by a non-linear function.