General Solution: A solution of a differential equation in which the number of arbitrary constants is equal to the order of the differential equation is called the general solution or complete integral or complete primitive.
Singular solution: A solution which can not be obtained from a general solution is called singular solution.
I have no objection on this two definition, both satisfy the given ODE and are clear to me and I have the idea how to find the general solution and the singular solution of an ODE.
My question is:
Although singular solution does not obtain from general solution (what is given in the definition), yet why it is called "general"?
I think my question is not a duplicate. If so please forgive me.
Thanks for your valuable time.