Definition:Differential Equation/Solution

Definition
Let $\Phi$ be a differential equation defined on a domain $D$.

Let $\phi$ be a function which satisfies $\Phi$ on the whole of $D$.

Then $\phi$ 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
Some sources refer to such a function $\phi$ as an explicit solution of $\Phi$.