Partial Differential Equation

A partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multi-variable function.

The function is often thought of as an “unknown” to be solved for, similar to how $x$ is thought of as an “unknown” number to be solved for in an algebraic equation such as $x^2 - 3x + 2 = 0$. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.