Solving dy/dx = (y-1)/x² with initial condition f(2) = 0

[stupefy07]

Homework Statement

Consider the differential equation dy/dx= (y-1)/x^2 and x does not equal 0
a. Find the particular solution y = f(x) to the differential equation with the initial condition f(2)=0
b. For the particular solution y = f(x) described in part a, find the limit as x goes to infinity of f(x)

Homework Equations

none

The Attempt at a Solution

not really sure where to begin.

Thank you so much!

 

[rock.freak667]

It is a separation of the variables type DE, can you solve one like that?

 

[ƒ(x)]

Try to get the dx and x together and then integrate

 

[naspek]

dy/dx= (y-1)/x^2

rearranging the equation, you will get...

∫1/(y - 1) dy = ∫1 / (x^2) dx