Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x, with initial condition y(1) = 1.

Answer 1

why all those useless words? Use some math symbols!

dy/dx = 3y/x

dy/y = 3/x dx
lny = 3lnx + c
or,
lny = ln(x^3) + ln(c) (different c)
y = cx^3
y(1)=1 means c=1

y = x^3

I expect that you can determine the domain for that...