Great question! Let's break down how this is typically handled in English mathematical contexts:

• First off, the super-long abbreviations like GSNHDE=GSHDE+SSNHDE are almost never used—they’re just too cumbersome to read, write, and remember. Mathematicians and students alike prefer concise, context-defined shorthand instead.
• A far more common approach is to define simple, intuitive symbols upfront, then use those consistently. For example:
  • Let G_h = General Solution of the Homogeneous Differential Equation (齐次微分方程通解)
  • Let G_{nh} = General Solution of the Non-homogeneous Differential Equation (非齐次微分方程通解)
  • Let P_{nh} = Particular Solution of the Non-homogeneous Differential Equation (非齐次微分方程特解)
    Note: In English, "Particular Solution" is the standard term for 特解, not "Special Solution"—using "Special Solution" might cause confusion in academic or technical contexts.
• With these definitions, the formula becomes clean and easy to follow:

  G_{nh} = G_h + P_{nh}
  

• If you need slightly more explicit abbreviations (for formal documents where you want minimal ambiguity), you might occasionally see things like GS(HDE) for the homogeneous general solution, GS(NHDE) for the non-homogeneous one, and PS(NHDE) for the particular solution. But even these are less common than the simple subscripted symbols above.

The key takeaway is that clarity and brevity win out—no one wants to scribble or type a 7-letter abbreviation just to refer to a solution type.

内容的提问来源于stack exchange，提问作者Bambinomio