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By: a guest on Jun 13th, 2012  |  syntax: None  |  size: 1.17 KB  |  hits: 12  |  expires: Never
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  1. Mathematica - DSolve spits out #1 in output
  2. eqs = {
  3. x1'[t] = a1*x1[t] + b1*y1[t]
  4. x2'[t] = a2*x2[t] + b2*y2[t]
  5. ...
  6. y1'[t] = c1*y1[t] + d1*x1[t]
  7. y2'[t] = c2*y2[t] + d2*x2[t]}
  8.        
  9. x1 -> e^(-ta1)
  10. x2 -> e^(-t)RootSum[a1a2+a3b4#1 + a3a1b2#1]
  11. ...
  12.        
  13. In[511]:= Integrate[1/(1 + x + x^2 + x^3 + x^4), x]
  14.  
  15. Out[511]= RootSum[1 + #1 + #1^2 + #1^3 + #1^4 &,
  16.  Log[x - #1]/(1 + 2 #1 + 3 #1^2 + 4 #1^3) &]
  17.        
  18. In[512]:= Normal[%]
  19.  
  20. Out[512]=
  21. Log[(-1)^(1/5) + x]/(1 - 2 (-1)^(1/5) + 3 (-1)^(2/5) - 4 (-1)^(3/5)) +
  22.   Log[-(-1)^(2/5) + x]/(
  23.  1 - 4 (-1)^(1/5) + 2 (-1)^(2/5) + 3 (-1)^(4/5)) +
  24.  Log[(-1)^(3/5) + x]/(
  25.  1 - 3 (-1)^(1/5) - 2 (-1)^(3/5) + 4 (-1)^(4/5)) +
  26.  Log[-(-1)^(4/5) + x]/(1 + 4 (-1)^(2/5) - 3 (-1)^(3/5) + 2 (-1)^(4/5))
  27.        
  28. In[513]:= Sum[
  29.  Log[x - t]/(1 + 2*t + 3 t^2 + 4 t^3), {t,
  30.   t /. {ToRules[Roots[1 + t + t^2 + t^3 + t^4 == 0, t]]}}]
  31.  
  32. Out[513]=
  33. Log[(-1)^(1/5) + x]/(1 - 2 (-1)^(1/5) + 3 (-1)^(2/5) - 4 (-1)^(3/5)) +
  34.   Log[-(-1)^(2/5) + x]/(
  35.  1 - 4 (-1)^(1/5) + 2 (-1)^(2/5) + 3 (-1)^(4/5)) +
  36.  Log[(-1)^(3/5) + x]/(
  37.  1 - 3 (-1)^(1/5) - 2 (-1)^(3/5) + 4 (-1)^(4/5)) +
  38.  Log[-(-1)^(4/5) + x]/(1 + 4 (-1)^(2/5) - 3 (-1)^(3/5) + 2 (-1)^(4/5))
  39.  
  40. In[514]:= % - %% // FullSimplify
  41.  
  42. Out[514]= 0
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