Homework Help: AP Test Practice DE

1. Feb 26, 2012

Alcubierre

1. The problem statement, all variables and given/known data

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).

2. Relevant equations

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

3. 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?

2. Feb 26, 2012

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.