 A linear differential equation that fails this condition is called inhomogeneous.A linear differential equation can be represented as a linear operator acting on "y(x)" where "x" is usually the independent variable and "y" is the dependent variable.Therefore, the general form of a linear homogeneous differential equation is 

formula_25where "L" is a differential operator, a sum of derivatives (defining the "0th derivative" as the original, non-differentiated function), each multiplied by a function  formula_26  of "x"