# Having trouble solving a particular differential equation [closed]

I have the following equation:

$$\frac{f(x)}{f'(x)}\left(f(x) + \frac{1+(f'(x))^2}{f''(x)}\right) = c$$

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

Mathematica handles this well and I'm able to plot it just fine using NDSolve, but only when $$c = 0$$. For any other value of $$c$$, I get errors and the plot comes out all wrong.

Can anyone help me here?

### Edit

An example of the code I used for NDSolve was:

s =
NDSolve[
{y[x]/y'[x] * (y[x] + (1+(y'[x])^2)/y''[x]) == 1, y[0] == 10, y'[0] == 0},
y, {x, -0.5, 0.5}]

## closed as off-topic by MarcoB, Henrik Schumacher, m_goldberg, Alex Trounev, bbgodfreyApr 7 at 20:43

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• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Henrik Schumacher, m_goldberg, Alex Trounev, bbgodfrey
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• Can you give the NDSolve[] code you used so people don't have to retype things for you? – J. M. is away Mar 31 at 1:44
• @J.M.isslightlypensive Sorry, I've added it now. – Matheus Andrade Mar 31 at 1:49
• I don't have any trouble evaluating your example expression. I running V11.3 on macOS 10.13.4. I suggest you try relaunching Mathematica and try with a fresh notebook. – m_goldberg Mar 31 at 2:07
• @m_goldberg That worked. Thanks. – Matheus Andrade Mar 31 at 2:16