Family of Curves w/ Slope=1 at (1,1) - Can You Answer?

[gikiian]

Just a question that came to my mind while studying differential equations.

Of-course this is a silly one (I think), but I wonder if someone can answer it!

Thanks

 

[HallsofIvy]

I'm not sure what you mean by "find" that family. A perfectly good answer is "the family of all f(x) such that f(1)= 1 and f'(1)= 1". But there are simply too many of them to be able to write a "formula".