Question

Is dy the same as d/dx?

Answer 1

technically no.

for certain cases it might be true, but avoid associating them like that

Answer 2

I'm pretty sure it's not. Because in a separable equation you have dy with all your y variables and dx with all your x variables. d/dx is the change of a certain function with respect to x, so if y was to come after the d/dx then yes it would be, but in general d/dx is not dy. 'dy' by itself is just the change of y.