AP Test Practice | DE Homework: Sketch Slope Field

[Alcubierre]

Homework Statement

Consider the differential equation $\frac{dy}{dx}$ = 2x - y

On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated, and sketch the solution curve that passes through the point (0, 1).

Homework Equations

$\frac{du}{dx}$ = u where u = 2x - y

The Attempt at a Solution

$\frac{dy}{dx}$ = 2x - y

$\frac{du}{dx}$ = u where u = 2x - y

u' = 2 - $\frac{dy}{dx}$Then what do I do? I have no clue where to go from here.
Is this a homogeneous differential equation?

I know what to do in regards to the rest of the problem, I just don't know how to separate so I can integrate. Do I use the substitution method or integrating factors?

 

[Dick]

du/dx isn't equal to u. dy/dx=u. What is du/dx? Try to write the differential equation completely in terms of u instead of y. Then separate it.