What does it mean when it says x dy/dx=(equation) y

As in what am i meant to do

well, I am not sure what this means if you said it correctly. anything with dy/dx is talking about calculus. If you are taking a differential equations class, you probably need to make it look like:

dy/y=dx/x

and you must integrate both sides: lnIyI + C = lnIxI + C

Not sure what to tell you from there. sorry

x(dy/dx) = y

Since you have a dy and a dx, you wil have to integrate it, but first you gotta manipulate the variables in the appropriate place.
x(dy/dx) = y
dy/dx = y/x
dy/y = dx/x

integrate both sides.
∫(1/y)dy = ∫(1/x)dx
ln|y| = ln|x| + C
ln|y| - ln|x| = C
ln|y/x| = C

Take e^ on both sides.
y/x = e^C
y = xe^C

Hope this helps :D

And if you were given an initial condition... you wanna plug your values in
at ln|y/x| = C, cuz thats when the C is the least affected.

maybe differentiate the equation?