Thread: 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

No, what you do is not correct.
Apply the usual method to solve a linear ODE : y'-y = 2x