In[]:=
ClearAll["Global`*"]​​​​(*ODE*)​​​​ode=D[β[ξ],{ξ,1}](1/Ln[f])*ω*
-β[ξ]
f
+μ+ν*
β[ξ]
f
​​​​(*Solutionه*)​​solution=DSolve[ode,β[ξ],ξ]​​
Out[]=
′
β
[ξ]
μ+
β[ξ]
f
ν+
-β[ξ]
f
ω
Ln[f]
Out[]=
β[ξ]
Log
-μ+
2
μ
-4νω
Tanh
1
2
-
2
μ
-4νω

1
Log[f]-
ξ
2
μ
-4νω
Log[f]
Ln[f]

2ν

Log[f]
