# Definition:General Solution

## Definition

Let $E$ be an equation in which $x$ is the independent variable.

The general solution of $E$ is the set of all $x$ that make $E$ a true statement.

### General Solution to Differential Equation

Let $\Phi$ be a differential equation.

The general solution of $\Phi$ is the set of all functions $\phi$ that satisfy $\Phi$.

## Also known as

A solution to an equation is also referred to as a solution of an equation.

Both forms can be found on $\mathsf{Pr} \infty \mathsf{fWiki}$, according to the tastes of the original contributors.