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Can someone show me how to Diff Eq?

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm not taking a de class, just curious.

    dy/dx = (-5x+10y)/(9x)

    y(1) = -2

    Use appropriate variable change to solve initial value problem.

    2. Relevant equations



    3. The attempt at a solution

    So, I'm given the derivative of function y, and want to know the actual function, with the condition that the original function when evaluated for 1 is negative 2, right?

    So, I integrate it, but I have two variables. What should I do?
     
  2. jcsd
  3. Sep 5, 2011 #2

    Pengwuino

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    Gold Member

    Well, you have two variables so you might guess that you're going to have to do two different integrals :)

    Typically the first line of attack is determining if a problem is what is called separable. In other words can you get your first order DE to look like

    [itex]f(y)dy = f(x)dx[/itex]

    At this point you would normally integrate both sides and then solve for y(x) with your initial conditions.

    I don't think this ones separable, though and the next method is using integrating factors. I suggest checking out http://www.khanacademy.org for some nifty videos on solving DEs
     
  4. Sep 5, 2011 #3
    So, I'm not allowed to just write it as a function of x? I figured that would be okay since the two variables are just x and y like any normal function, no extra one.
     
  5. Sep 5, 2011 #4

    Pengwuino

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    What do you mean?
     
  6. Sep 5, 2011 #5
    If the derivative is:

    y = (-5x + 10y) / (9x)

    Isn't that the same as

    y = (5x) / (9x-10)?

    Is that allowed?
     
  7. Sep 5, 2011 #6

    Pengwuino

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    No, that's not right

    [itex]y'(x)=(-5x+10y)/9x[/itex]

    THAT is the derivative. y'(x) and y(x) aren't the same thing.
     
  8. Sep 5, 2011 #7
    I figured that made the difference. thanks for the links!
     
  9. Sep 5, 2011 #8
    Since the problem says to use a variable change, you can try u = y/x, then the resulting DE becomes separable.
     
  10. Sep 5, 2011 #9

    Pengwuino

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    Gold Member

    oops didn't even notice that part of the question!
     
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