differential equation

A differential equation is an equation involving the first or higher derivatives of the function to be solved for.
If the equation only involves first derivatives it is called an equation of order one, and so on.
If only $n$-th powers of the derivatives are involved, the equation is said to have degree $n$. Equations of degree one are called linear.
Equations in only one variable are called ordinary differential equations to distinguish them from partial differential equations.