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