# Thread: y = f(y) ?

1. Hi, I'll start calculus next year but I am trying to self-teach.

I was wondering what is called a function in which the increment of y (derivative) is not based on x but on y itself.
If that is not clear, consider a function in which x is time and y is space t*v, if v =1 then the derivative of space is constant = 1.
If we consider the increment of space with respect to space, then the increment is not constant and is 1/y. so y(t+1)= y(t)+1/y

Probably this is a mess, I hope you can help me and say it this exists and has a name or how it shoud be formulated.  2. ### Related Discussions:

3. An autonomous differential equation is a differential equation which does not explicitly depend on the independent variable.  4. It is y'/y  5. Originally Posted by KJW An autonomous differential equation is a differential equation which does not explicitly depend on the independent variable.
Thanks, I googled that and found it's an autonomous system, can you tell me how to formulate it correctly, is this the only way?

An autonomous system is a ...of the form where x takes values...

Can I say y(tn+1)= y(tn)+1/y(tn)  6. Can I say y(tn+1)= y(tn)+1/y(tn)

I think your equation holds true if you replace the with , where is very small and approaching 0.

The problem with your equation is you have assumed that the rate of change of y at to be constant in the interval between , which need not be the case. means that the rate of change of the function x depends on the value of x at t. The moment t changes, the rate of change of the function takes a new value, which need not be same.  7. This post is old, but I'd almost like to bargain that Password's password for his account is Username...  Bookmarks
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