Hi, I just had my ordinary differential equation final exam today (summer class), the exam was fine. We had a bonus question though, it was a nonlinear second order differential equation, we didn't learn anything about those except for one existence and uniqueness theorem. I am curious if I got it right. The question was, solve: x2y''-4(y')2=0 Clearly C (constant) is a solution, for the other solution I made an educated guess that y is x2, that didn't quite work, but I figured out it was x2/8...so I put y=x2/8 + C I know this solution works because I've plugged it in, the thing I am wondering is when I solve it on wolframalpha.com it gives y[x] = -4 ln(C1x-4)/(C12)-x/C1+C2. I have noticed that these two solutions (mine and wolframs) are linearly independent, but since the equation is nonlinear I don't think combining the two would also be a solution....so I am just wondering if I got the answer right? Also, why doesn't wolfram also give my answer. I mean is it not a completely right answer? I guess the same rules don't apply to nonlinear and linear equations, could there be other answers as well? Thanks!