| 单词 | particular integral |
| 释义 | > as lemmasparticular integral particular integral n. Mathematics (a) a solution of a differential equation obtained by assigning values to the arbitrary constants of the complete primitive of the equation; †(b) a solution of a differential equation that cannot be obtained by assigning values to any or all of the arbitrary constants of the complete primitive; a singular solution (obsolete). ΘΚΠ the world > relative properties > number > calculus > [noun] > differential calculus > differential equations > solutions particular integral1814 Bessel function1872 Mathieu function1915 1814 P. Barlow New Math. & Philos. Dict. Particular Integral, in the Integral Calculus, is that which arises in the integration of any differential equation, by giving a particular value to the arbitrary quantity or quantities that enter into the general integral. 1820 G. Peacock Coll. Examples Differential & Integral Calculus ii. xi. 477 A particular integral of the original equation, involving only one arbitrary function. a1832 Encycl. Metrop. (1845) II. 23 This value of y satisfies the proposed equation; but as it cannot be derived from the complete integral we have obtained above by assuming a particular value for one of the arbitrary constants, it ought to be considered as a particular integral. 1946 L. Toft & A. T. J. Kersey Theory of Machines (ed. 5) xiv. 417 If X is a fuction of t, which satisfies (1), it is known as a particular integral. 1997 Proc. Royal Soc. A. 453 2612 On transforming back to u we have a particular integral of the form up = ap/ 0 +ap/ 1w +ap/ 2w2 + …, where the ap/ i are just constant vectors. < as lemmas |
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