Question

Find the particular solution y=f(x) to the differential equation y'=1+y/x with the initial condition f(-1)=1

I would appreciate any help

Answer 1

separate variables:
dy/dx(1/(1+y))=1/x
dy/(1+y)=dx/x)
integrate bouth sides:
Ln|1+y|=Ln|x| + LnC
1+y=Cx
y=Cx-1
now use initial condition: 1=C(-1)-1
from here C=-2
so your solution is:
y=-2x-1

Answer 2

Thank you.

Answer 3

How would I go about finding domain from here ?