The general solution to a differential equation must satisfy both the homogeneous and non-homogeneous equations. It is the nature of the homogeneous solution that the equation gives a zero value. The general solution of a differential equation is also called the primitive. The general solution or primitive of a differential equation of order n always contains exactly n essential arbitrary constants.
A particular solution differential equation contains two or more independent variables. The derivatives occurring in the equation are partial derivatives. A differential equation is a solution of a differential equation containing no arbitrary constants.