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^{2}. I want to take the second derivative to get some information about the concavity of the solution, but I can't wrap my head around what's really going on.

What I think I know: I have an ODE that is dependent on the dependent variable, so my solution will only change with changes in the value of y.

What I want to know: How is dy/dx (the derivative of y(x) with respect to x) dependent completely on y? How do I take the second derivative with respect to x when I have no x in the first derivative? Do I have an x nested in y in the derivative?

I get the feeling I'm missing something really simple. If you find it enough to just give me a hint, I'm definitely cool with that. More in depth answers are awesome too.