Tracing – Having trouble solving a particular differential equation

I have the following equation:

$$ frac {f (x)} {f (x)} left (f (x) + frac {1+ (f (x)) ^ 2} {f & # 39; ; (X)} right) = c $$

or $ c $ is a constant $> 0 $.

Mathematica handles this very well and I am able to trace it very well using NDSolvebut only when $ c = $ 0. For any other value of $ c $I receive errors and the plot is completely wrong.

Can any one help me?

edit

Here is an example code I used for NDSolve:

s =
NDSolve[
   {y[x]/ y & # 39;[x] * (y[x] + (1+ (y & # 39;)[x]) ^ 2) / y & # 39; & # 39;[x]) == 1, there[0] == 10, y & # 39;[0] == 0},
y, {x, -0.5, 0.5}