One partial solution of the non-homogeneous equation: d 2 x ( t ) d t 2 + c ¯ ¯ d x ( t ) d t + k ¯ ¯ x ( t ) = p ¯ ¯ ( t ) , where p ¯ ¯ ( t ) = p ( t ) m , could be obtained by the Lagrangian method for deriving partial solution of non-homogeneous ordinary differential equations.