The "notational second derivative" is true only when the function 𝑓(𝑥) is of a very specific form 
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that's what the ln(c) is in there for ;)
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But you need something to "turn off" the 'x' dependence, right? Like what choices of parameters give f(x)=2? I think just moving the constant to be in front of the x would fix it(?)
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what i'm saying is that the full solution is y(x) = c -ln(x+b) and i just wrote c--> ln(c) for compactness
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