Definition:Differential Equation/Solution/Historical Note
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Historical Note on Solution to Differential Equation
The original name for a solution to a differential equation that Jacob Bernoulli used in $1689$ was integral.
Leonhard Paul Euler used the term particular integral in his Institutiones Calculi Integralis of $1768$, but the latter term has more recently taken on a more precise definition.
The term solution was first used by Joseph Louis Lagrange in $1774$.
This terminology became established under the influence of Jules Henri Poincaré.
Sources
- 1926: E.L. Ince: Ordinary Differential Equations ... (previous) ... (next): Chapter $\text I$: Introductory: $\S 1.2$ Genesis of an Ordinary Differential Equation (footnote $\dagger$)