Why does a particular solution of a non homogeneous ODE called a particular solution Why does the particular solution of non homogeneous ODE called a "particular solution" ? 
Is it called in this way because it depends on the function that exists in the non homogeneous part ?

It is called that because in order to find the general solution, it is enough to find just one solution to the non-homogeneous problem, and then add the general homogeneous solution to it. To put it another way, we don't need to go hunting for lots of non-homogeneous solutions directly in order to solve a non-homogeneous linear equation, we just need one particular one, and then we can build all the others.
