〈 Berger | Dillon 〉

Or a constant function :)

that's what the ln(c) is in there for ;)

so i t covers both cases

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(?)

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

Yeh but f(x)=2 is also a solution but not covered by this, right?

absolutely it is.. this is the most general solution to the 2nd order ode, and you can certainly find initial conditions to make it a "particular" solution, which is what you're asking for..