First-order differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form

where ${\displaystyle a_{0}(x)}$, ..., ${\displaystyle a_{n}(x)}$ and ${\displaystyle b(x)}$ are arbitrary differentiable functions that do not need to be linear, and ${\displaystyle y',\ldots ,y^{(n)}}$ are the successive derivatives of the unknown function y of the variable x.

...
Wikipedia