Particular Solution

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particular solution [pər¦tik·yə·lər sə′lü·shən]

(mathematics)

A solution to an ordinary differential equation obtained by assigning numerical values to the parameters in the general solution. Also known as particular integral.

Particular Solution

A particular solution of a differential equation F (x, y, y′, . . ., y⁽ⁿ⁾) = 0 is a solution y = Φ(x) obtained from the general solution y = Φ(x, C₁, . . ., C_n) of the equation for some specific choice of the arbitrary constants C₁, . . ., C_n. For example, the general solution of the equation y^″ + y = 0 is y – C₁ cos x + C₂ sin x; if we set C₁ = 2 and C₂ = –1, we obtain the particular solution y = 2 cos x – sin x.

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