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, . . ., 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 yC1 cos x + C2 sin x; if we set C1 = 2 and C2 = –1, we obtain the particular solution y = 2 cos x – sin x.

References in periodicals archive ?
On the other hand, the question of the stability of particular solutions of the Einstein equations in the wake of the groundbreaking proof of the stability of the Minkowski space-time due to D.
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Therefore the obtained particular solutions for the bimorph converter were compared with the literature-derived solution.
The intent is to look at problems and alternatives, not to advocate particular solutions.
As a theological ideal, Christianity may be regarded as an absolute; but, as a human endeavor, it demands particular solutions to these various conflicts.
Cirnu, Determination of particular solutions of non-homogeneous linear differential equations by discrete deconvolution, UPB Scientific Bulletin, A, 69 (2007) 2, 3-16
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With common agreement, effective and particular solutions can be found upon which we can all agree on," Christofias said.
0] are some particular solutions of (2) and T is arbitrary element of the ring [R.
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The capability to deliver these particular solutions and implement them quickly was an overwhelmingly positive factor in our success.