Well I am not sure if I really need to differentiate this equation but in my other class exercise we differentiate dy/dx + y = 2x to 2x-y !
This is not differentiating... this is just solving for dy/dx (which you want to do). In your problem you already have dy/dx as a function of x and y.
so I thought I need to differentiate dy/dx = 3 - y/x too ! so I was confused with all, Am I wrong?
If I don't need to then I can carry on using Euler method!?
no you don't need to differentiate and you can use Euler's method. Just follow the outline in your book, notes or the link I provided above.