Definition:Differential Equation/Solution/General Solution

Definition
Let $\Phi$ be a differential equation.

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

Also known as
The general solution of 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 of $\Phi$.

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

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

The term solution set is sometimes encountered.

Also see

 * Definition:Solution of Differential Equation
 * Definition:Particular Solution of Differential Equation
 * Definition:Singular Solution to Differential Equation