From: nma@12000.org   
      
   On 4/28/2016 7:44 PM, Dr Huang wrote:   
   > I did try it on wolfram alpha but it did not work. can u try it on   
   Mathematica ?   
   >   
   > math.DrHuang.com   
   >   
      
   some ODE solutions are given in implicit form as in this case.   
      
   In Mathematica, this is when the solution to the ode   
   has y(x)->Solve[...] in it, and in Maple, when the solution   
   has y(x)=RootOf(...).   
      
   Maple has the odetest() function which is able to verify   
   the ode solution against the ode itself, even when the solution   
   has RootOf() in it. Mathematica does not have such function,   
   but one can normally verify the solution to simple ode's by   
   using the ReplaceAll[] command, as in   
      
   eqn = y'[x] == x;   
   sol = DSolve[eqn, y, x];   
   eqn /. sol   
                 {True}   
      
      
   When the solution to ODE has Solve[...] in it, as in 84,   
   the above method does not work. But this does not mean   
   the implicit solution given by Mathematica is wrong, it   
   means someone has to do more work to verify it, by   
   some other means, or just trust Mathematica.   
      
   If you think Mathematica solution to 84 is not correct,   
   then this is a bug and you can report it to support@wolfram.com   
   for Maple, bug reports should be send to support@maplesoft.com   
      
   The solutions (if CAS returns one) are not verified to be   
   correct in the report. If a solution is given, it is   
   assumed the solution is correct. Only when the ode returns   
   unevaluetd, or if the solution contains DifferentialRoot (for   
   Mathematica) or DESol (for Maple), or it times out, then the   
   problem is marked as not solved.   
      
   Verifying solutions are correct, is left as an exercise   
   to the interested reader and is beyond the scope of   
   the report.   
      
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)