Why 它不能得到正确的结果

[TankGun]

请各位高手给看看,为什么?应该怎么作?

[liu16]

不知道是不是这个意思.
In[1]:= U[\[Xi]_] := \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 0\), \(2\)]\(\[Alpha][m]
\*SuperscriptBox[\((
\*FractionBox[\(\(G'\)[\[Xi]]\), \(G[\[Xi]]\)])\), \(m\)]\)\)

In[2]:= U'[\[Xi]]

Out[2]= -((\[Alpha][1]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]^2)/G[\[Xi]]^2) - (2 \[Alpha][2]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]^3)/G[\[Xi]]^3 + (\[Alpha][1]
\!\(\*SuperscriptBox["G", "\[Prime]\[Prime]",
MultilineFunction->None]\)[\[Xi]])/G[\[Xi]] + (2 \[Alpha][2]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]
\!\(\*SuperscriptBox["G", "\[Prime]\[Prime]",
MultilineFunction->None]\)[\[Xi]])/G[\[Xi]]^2

In[3]:= t = G''[\[Xi]] -> -\[Lambda] G'[\[Xi]] - \[Mu] G[\[Xi]]

Out[3]=
\!\(\*SuperscriptBox["G", "\[Prime]\[Prime]",
MultilineFunction->None]\)[\[Xi]] -> -\[Mu] G[\[Xi]] - \[Lambda]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]

In[4]:= %% /. t

Out[4]= -((\[Alpha][1]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]^2)/G[\[Xi]]^2) - (2 \[Alpha][2]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]^3)/
G[\[Xi]]^3 + (\[Alpha][1] (-\[Mu] G[\[Xi]] - \[Lambda]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]))/G[\[Xi]] + (2 \[Alpha][2]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]] (-\[Mu] G[\[Xi]] - \[Lambda]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]))/G[\[Xi]]^2

In[5]:= PowerExpand[% // Apart // Cancel, G'[\[Xi]]/G[\[Xi]]]

Out[5]= -\[Mu] \[Alpha][
1] - ((\[Lambda] \[Alpha][1] + 2 \[Mu] \[Alpha][2])
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]])/
G[\[Xi]] - ((\[Alpha][1] + 2 \[Lambda] \[Alpha][2])
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]^2)/G[\[Xi]]^2 - (2 \[Alpha][2]
\!\(\*SuperscriptBox["G", "\[Prime]",
MultilineFunction->None]\)[\[Xi]]^3)/G[\[Xi]]^3