Non-homogeneous differential equation - nomenclature

Question

I need to translate into English the abbreviation of the following general formula:

General Solution of the Non-homogeneous Differential Equation = General Solution of the Homogeneous Differential Equation + Special Solution of the Non-homogeneous Differential Equation

Is in English language the following abbreviation (or any other) used?

GSNHDE=GSHDE+SSNHDE

Answer 1

I didn't read this type of abbreviation type in standard ODE books. However the general solution of Non-homogeneous ODE can be written in the form

$$y=y_c+y_p$$
where $y_c$ is solution of the corresponding homogeneous equation and $y_p$ is solution of non-homogeneous part of the ODE, which are also known as complementary function and particular integral respectivly.