Particular Solution

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, . . ., Cn) of the equation for some specific choice of the arbitrary constants C1, . . ., Cn. 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.