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.