Can't get same answer as given by Wolframalpha

[RobinM]

I need help with an equation
2y’’y=(y’)²+1
I think i found the answer
I end up with
(1/c1)2sqrt(c1y-1)= -x+c2
Or
(1/c1)2sqrt(c1y-1)= x+c2
Now when i try to solve for y i can’t get to the solutiongiven by Wolframalpha
y= (1/4c2)(c1²+1)x² +c1x +c2


can anyone plz tell me how to get there or tell me what i did wrong?

 

[HallsofIvy]

Since Wolfram alpha's solution has been solved for y and yours hasn't, have you tried squaring both sides of your solution as a start to solving for y?