From: nma@12000.org   
      
   On 1/27/2021 5:05 PM, drhu...@gmail.com wrote:   
   > what is solution of  y''-y' y-2x=0  and  how to test it by online software?   
   > it is seems wolfram solution is wrong?   
   >   
   > mathHand.com   
   >   
      
   I do not try Wolfram alpha, but Mathematica solves this. I assume   
   answer it gives is correct.   
      
   Here is how to solve this by hand.   
      
   Integrate both sides w.r.t. x   
      
   int ( y''-y' y ,x) = int( 2 x,x)   
      
             -y^2/2 + y' = x^2 + C   
      
   This is first order ode   
      
             y' = C + x^2 + y^2/2   
      
   Compare to https://en.wikipedia.org/wiki/Riccati_equation  shows it is RICCATI   
      
          y' = q0(x) + q2(x) y^2   
      
   with missing q1(x). Here q0=c+x^2 abd q2(x) = 1/2.   
      
   This has standard method of solving as shown in the above wiki page.   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)