Definition:Differential Equation/Solution

Definition
Let $\Phi$ be a differential equation.

Any function $\phi$ which satisfies $\Phi$ is known as a solution of $\Phi$.

Note that, in general, there may be more than one solution to a given differential equation.

On the other hand, there may be none at all.

Also known as
A solution of a differential equation can also be referred to as a solution to a differential equation.

Such a solution is known as a particular solution.

Some sources refer to such a solution as a specific solution.

Also see

 * Definition:Solution Set of Differential Equation: the set of all solutions to a differential equation.