Lacroix and the Calculus

Volume 35 of the series Science Networks. Historical Studies pp 179-256

Types of solutions of differential equations

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This chapter deals with several aspects of differential equations relating to types of solutions (complete, general, particular, and singular integrals or solutions), as opposed to methods of solution. That is, the subject here is not so much the processes for solving differential equations, as the conceptions about what kind of object a final solution might be. For this reason, the word “solution” will be used here in the sense of answer, but not in the sense of process for obtaining an answer.