Differential Equations Classification Ordinary/Partial involving only ordinary derivatives with respect to a single independent variable is called an ordinary differential equation. involving partial derivatives with respect to more than one independent variable is a partial differential equation. Linear/Non-linear Linear: One in which the dependent variable \(y\) and its derivatives appear in additive combinations of their first powers. May be written in the form \[ a_{n}(x) \frac{d^{n} y}{d x^{n}}+a_{n-1}(x) \frac{d^{n-1} y}{d x^{n-1}}+\ldots+a_{1}(x) \frac{d y}{d x}+a_{0}(x) y=F(x) \]