From: nma@12000.org   
      
   If one has a separable ode, first order, such as this:   
      
   eq:= diff(y(x),x) = (a4*x^4+a3*x^3+a2*x^2+a1*x+a0)^(-1/2);   
      
   Maple gives the answer with simply integrating the RHS, but   
   leaves the integral unevaluated.  Would you consider this as solved   
   or not?  Here is Maple solution to the above ode   
      
      result:= y(x) = Int(1/sqrt(a4*x^4+a3*x^3+a2*x^2+a1*x+a0), x)+_C1   
      
   The answer is of course correct from math point of view,   
   and it passes the test:   
      
         r := odetest( result,eq );   
      
   But if the integral is not actually solved, should one consider   
   this as valid solution to an ode? This means all ode's of the form   
   y'(x) = f(x) can be considered solved, by just adding an integral to   
   RHS and a constant, even if the CAS can't solve the integral.   
      
   Mathematica gives this   
      
   DSolve[-(1/Sqrt[a0 + a1*x + a2*x^2 + a3*x^3 + a4*x^4])+ y'[x] == 0, y[x], x]   
      
   y[x] -> C[1] - (2 EllipticF[   
         ArcSin[Sqrt[(((x -   
             Root[a0 + a1 #1 + a2 #1^2 + a3 #1^3 + a4 #1^4 &, 1]) (Root[   
              a0 + a1 #1 + a2 #1^2 + a3 #1^3 + a4 #1^4 &, 2] -   
             Root[a0 + a1 #1 + a2 #1^2 + a3 #1^3 + a4 #1^4 &, 4]))/((x -   
             Root[a0 + a1 #1 + a2 #1^2 + a3 #1^3 + a4 #1^4 &, 2]) (Root[   
              a0 + a1 #1 + a2 #1^2 + a3 #1^3 + a4 #1^4 &, 1] -   
             Root[a0 + a1 #1 + a2 #1^2 + a3 #1^3 + a4 #1^4 &, 4])))]   
   ..... too long to show....   
      
      
   I was just wondering what is the view on this. Would you consider   
   this as "solved" or not? I am updating my Kamke ODE tests, and   
   needed to make sure I grade Maple as pass for this or no.   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)