title: Mathematica - DSolve spits out #1 in output
body: <p>I'm not quite certain how to go about interpreting this.</p>
  
  <p>I'm solving a fairly large system of differential equations, DSolve <em>sometimes</em> spits out a list of replacement rules that include terms that have a <code>#1</code> . I know that <code>#1</code> is a placeholder for an argument, but I just have no clue where it comes from.</p>
  
  <p>If I have a system of equations similar to </p>
  
  <pre><code>eqs = {
  x1'[t] = a1*x1[t] + b1*y1[t]
  x2'[t] = a2*x2[t] + b2*y2[t]
  ...
  y1'[t] = c1*y1[t] + d1*x1[t]
  y2'[t] = c2*y2[t] + d2*x2[t]}
  </code></pre>
  
  <p><code>DSolve[eqs,vars,t]</code> spits out something like</p>
  
  <pre><code>x1 -&gt; e^(-ta1)
  x2 -&gt; e^(-t)RootSum[a1a2+a3b4#1 + a3a1b2#1]
  ...
  </code></pre>
  
  <p>Obviously a little more complicated but you get the point. </p>
  
  <p>Nothing in the documentation hints as to why this is occurring, And it only happens under certain permuations of parameters (e.g. when I play around with parameters in the original system it either works or doesn't)</p>