The "notational second derivative" is true only when the function 𝑓(𝑥) is of a very specific form 
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Or a constant function :)
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so i t covers both cases
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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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No he's right. This is assuming the initial condition isn't y'(0)=0. If it is, then y(x) ≡ K.
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y' = y² is a very popular example of a simple ODE whose general formula doesn't cover all solutions
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