In[2]:= DSolve[{y'[x] == x*Log[x], y[1] == 1}, y[x], x]
Out[2]= {{y[x] -> 1/4 (5 - x^2 + 2 x^2 Log[x])}}
In[3]:= Dimensions[%]
Out[3]= {1, 1}
and that works
In[5]:= Clear[a]
a = DSolve[{y'[x] == x*Log[x], y[1] == 1}, y[x], x];
In[7]:= a[[1]]
Out[7]= {y[x] -> 1/4 (5 - x^2 + 2 x^2 Log[x])}
In[11]:= g[q_] := (y[x] /. a[[1]]) //. x -> q
In[12]:= g[1]
Out[12]= 1
Observe the SetDelayed in the definition of g and how the variable q enters after the replacement.
