# Linear differential equation

From AMS Glossary

## linear differential equation

A differential equation that is linear in the dependent variable and derivatives thereof.

The existence of a wealth of mathematical techniques and tables for the treatment of linear equations guarantees that a physical problem representable by such an equation is very much easier to solve and understand than a nonlinear one. The advection terms in the fundamental equations of hydrodynamics are not linear (strictly, they are "quasi-linear"), and much of dynamic meteorology has been an attempt to circumvent this difficulty.