From: nma@12000.org   
      
   On 7/9/2022 1:43 AM, Dr Huang wrote:   
   > wolfram gives   
   > (c1-x)^2/x   
   > is it right? did it seem wrong? what is yours?   
   >   
   > DrHuang.com   
      
   Mathematica 13.1   
      
   ClearAll[x, y]   
   ode = x*y'[x] + y[x] == 2*(x*y[x])^(1/2);   
   sol = DSolve[ode, y[x], x, IncludeSingularSolutions -> True]   
      
   gives   
      
   {{y[x] -> (E^(C[1]/2) + x)^2/x}, {y[x] -> x}}   
      
   The first is the general solution and the second is singular solution.   
      
   The solution you give is a particular solution which satisfies the ode   
   under the condition x>=C[1] only. You can see this by doing   
      
   sol = y -> Function[{x}, (C[1] - x)^2/x]   
   result = ode /. sol // FullSimplify   
      
              Sqrt[(x - C[1])^2] + C[1] == x   
      
   The above becomes identity when x >= C[1]   
      
   ps. I do not use Wolfram Alpha.   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)