A particular solution of a differential equation is any single function that satisfies the equation, with any initial conditions or boundary conditions under consideration. It is distinguished from a family containing all solutions.
For a linear nonhomogeneous differential equation ![L[y]=f](/images/equations/ParticularSolution/Inline1.svg)
,
if 
is a particular solution and 
is any solution of the associated homogeneous differential
equation ![L[y]=0](/images/equations/ParticularSolution/Inline4.svg)
,
then 
is also a solution of ![L[y]=f](/images/equations/ParticularSolution/Inline6.svg)
. Conversely, the difference of any two particular solutions
satisfies the associated homogeneous differential equation.
