# Definition:Differential Equation/Solution/General Solution

## Definition

Let $\Phi$ be a differential equation.

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

## Also known as

The general solution to a differential equation $\Phi$ can also be referred to as the solution of $\Phi$, but beware of confusing this with the concept of a solution to $\Phi$.

The general solution to a differential equation can also be referred to as the general solution of a differential equation.

Some sources refer to this general solution as a general integral.

The term solution set is sometimes encountered.

## Also see

• Results about general solutions to differential equations can be found here.

## Historical Note

The general solution to a differential equation was formerly known as the complete integral, or complete integral equation.

The Latin term used by Leonhard Paul Euler was æquatio integralis completa.

However, the term integral equation is now used to mean something completely different, and should not be used in this context.