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> y(x) = f(x,y), y(x0) = y0

If this is supposed to be the ODE definition, shouldn't it be y'(x) = f(x,y)? Otherwise I don't quite understand the definition of 'f'.

Thanks for pointing this out. It is indeed a typo.

I noticed the same thing. I presume it is a typo. Later on f is defined as you would expect.