In[]:=
solhomo=DSolve[y'[x](x-y[x])/(x+y[x]),y[x],x]
Out[]=
y[x]-x-
2

1

+2
2
x
,y[x]-x+
2

1

+2
2
x

In[]:=
y[x_]=y[x]/.solhomo[[1,1]]
Out[]=
-x-
2

1

+2
2
x
In[]:=
y[x_,c1_]:=y[x]/.{C[1]c1};
In[]:=
funcionesh=Table[y[x,c1],{c1,0,3}]
Out[]=
-x-
1+2
2
x
,-x-
2

+2
2
x
,-x-
4

+2
2
x
,-x-
6

+2
2
x

In[]:=
famh=Plot[funcionesh,{x,-5,5},PlotRange{-30,0},AxesLabel{"x","y"},AxesStyleBlack]
Out[]=
In[]:=
campoh=VectorPlot[{(x-y)/(x+y),x},{x,-5,6},{y,-30,20},AxesTrue,AxesStyleBlack,AxesBlack]
Out[]=
In[]:=
Show[{famh,campoh}]
Out[]=