Defining an ordinary differential equation

Question

I was asked to define the term 'ordinary differential equation.'

Can someone please verify whether this definition is correct? Thanks!

Here it is:

Ordinary Differential Equation: A differential equation that contains one or more functions with one independent variable and its derivatives. (Source: Wikipedia). For example, the equation can be of the form $F_n(x)y^{(n)}+F_{n−1}(x)y^{(n−1)}+...+F_1(x)y′+F_0(x)y=g(x)$ where $F_n, F_{n-1}, F_1, F_0, g$ are functions in terms of $x$.

Answer 1

An ODE is an equation of the form $$ F(x,y,y',\ldots,y^{(n)})=0, $$ where $\,'=\dfrac{d}{dx}$. In fact, the above is an $n-$th order nonlinear ODE.

An linear ODE is an equation of the form $$ y^{(n)}+p_{n-1}(x)y^{(n-1)}+\cdots+p_0(x)y=q(x). $$