From: nma@12000.org   
      
   >   
   >   why wolfram cannot find simple solution in many equations? many examples,   
   e.g.:   
   > 1/x*y"-y-x^2=0   
   > 1/x*y"-y-x^3=0   
   > 1/x*y"-y-x^4=0   
   >   ......   
   >   
   > mathHand.com can:   
   > http://server.drhuang.com/input/?guess=dsolve%281%2Fx*ds%28y%2   
   x%2C2%29-y-x%5E3%29   
   >   
   > so it is good idea to use two software to check solution.   
   >   
      
   For the first ode above. This is inhomogeneous Airy ode. The solution you give   
   for   
      
                1/x*y''[x]-y[x]-x^2==0   
      
   is   
      
                y(x)= -6+Ai(x)*C1+Bi(x)*C2-x^3   
      
   But this solution is not verified by Maple:   
      
   ==============   
   restart;   
   ode := 1/x*diff(y(x),x$2) - y(x) - x^2 = 0;   
   sol := y(x) = -6+AiryAi(x)*_C2 + AiryBi(x)*_C1-x^3;   
   odetest(sol,ode);   
      
                  x^3 - x^2   
   =================   
      
   Which is not zero. Hence not a valid solution?   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)