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Homework Help: Solving dy/dx=x-y

  1. Mar 15, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\int (x-y) [/tex]

    What is [tex]\int y[/tex] ? I don't mean [tex]\int y dy[/tex].

    3. The attempt at a solution

    [tex]dy/dx = x-y[/tex]
    [tex]y + dy = x dx[/tex]
    [tex]\int y + \int dy = \int x dx[/tex]
    [tex]\int y + y = x^2/2 + c[/tex]

    I am stuck at this point because I don't know how to integrate y without respect to anything...If that even makes sense.

    EDIT:

    Nvm...I am stupid xD

    [tex]\int x dx - \int y dx [/tex]
     
    Last edited: Mar 15, 2010
  2. jcsd
  3. Mar 15, 2010 #2

    gabbagabbahey

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    That still doesn't help you though. How exactly do you plan on integrating [itex]\int y(x) dx[/itex] when you don't know what [itex]y(x)[/itex] is?

    You can't solve this differential equation just by integrating both sides. Instead, try using the substitution [itex]u=x-y[/itex] to rewrite the DE in terms of [itex]u(x)[/itex] and [itex]u'(x)[/itex].
     
  4. Mar 15, 2010 #3

    D H

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    That will result in another nonhomogeneous ODE. A tiny bit simpler perhaps, but still nonhomogeneous.

    computerex: What have you been taught regarding solving nonhomogeneous differential equations?
     
  5. Mar 15, 2010 #4

    gabbagabbahey

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    Something about separable ODE's appeals to me though:wink:
     
  6. Mar 15, 2010 #5

    D H

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    Depends on the OP's background. The original problem can be rewritten as

    [tex]\frac{dy}{dx} + y = x[/tex]

    The homogeneous and particular solutions can be read off just by inspection.
     
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