Is this differential equation separable?

Can we apply Separation of Variables to this differential equation?

y' = 2x + y

I tried to apply Separation of Variables:

dy

dx = 2x + y

subtracted y on both sides:

dy

dx - y = 2x

multiply both sides by dx:

dy - y = 2x dx

**My question is does the dx get multiplied to the y as well, so that it would look like this:**

dy - ydx = dx dx

Re: Is this differential equation separable?

No, what you do is not correct.

Apply the usual method to solve a linear ODE : y'-y = 2x