# y = f(y) ?

• July 7th, 2014, 02:13 AM
y = f(y) ?
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.
• July 7th, 2014, 03:50 AM
KJW
An autonomous differential equation is a differential equation which does not explicitly depend on the independent variable.
• July 7th, 2014, 04:07 AM
whizkid
It is y'/y
• July 7th, 2014, 04:59 AM
Quote:

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

Can I say y(tn+1)= y(tn)+1/y(tn)
• July 7th, 2014, 09:31 AM
HyD@

Quote:

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.
• August 14th, 2014, 02:55 PM
MindlessMath
This post is old, but I'd almost like to bargain that Password's password for his account is Username...