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.
Let $S$ denote the solution set of $\Phi$.
The term solution was first used by Joseph Louis Lagrange in $1774$.
This terminology became established under the influence of Jules Henri Poincaré.
- 1926: E.L. Ince: Ordinary Differential Equations ... (previous) ... (next): Chapter $\text I$: Introductory: $\S 1.2$ Genesis of an Ordinary Differential Equation
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 1.2$: General Remarks on Solutions
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: differential equation