Question

Which of the following is the general solution of the differential equation dy dx equals the quotient of 8 times x and y?

Answer 1

do you mean product of x and y?

dy/dx = 8 x y

or do you mean
dy/dx = 8 x / y

or what ?

if the latter then
y dy = 8 x dx

y^2/2 = 8 x^2/2 + C

y^2 - 8 x^2 = constant

Answer 2

y'=8x/y

separation of variables...

y dy = 8x dx
1/2 y^2 + C=8/2x^2 + K

looks to me the general solution is

y^2=8 x^2 + K

check:
2ydy=16x dx
dy/dx=8x/y

Answer 3

We agree, if that is indeed the question :)