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Homework Help: AP Test Practice DE

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider the differential equation [itex]\frac{dy}{dx}[/itex] = 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

    [itex]\frac{du}{dx}[/itex] = u where u = 2x - y

    3. The attempt at a solution

    [itex]\frac{dy}{dx}[/itex] = 2x - y

    [itex]\frac{du}{dx}[/itex] = u where u = 2x - y

    u' = 2 - [itex]\frac{dy}{dx}[/itex]

    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. jcsd
  3. Feb 26, 2012 #2


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    Science Advisor
    Homework Helper

    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.
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