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First Order Homogeneous Differential Equations

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the general solution of the following homogeneous differential equations:

    (i) [tex]\frac{du}{dx} = \frac{4u-2x}{u+x}[/tex]
    (ii) [tex]\frac{du}{dx} = \frac{xu+u^{2}}{x^{2}}[/tex]

    (You may express your solution as a function of u and x together)

    2. Relevant equations

    There are no relevant equations to this solution

    3. The attempt at a solution

    (i) [tex]\frac{du}{dx} = 4 - \frac{6x}{u+x}[/tex]
    I could then use the substition y=u+x with dy/dx = du/dx + 1 to give:
    [tex]\frac{dy}{dx} = 5 - \frac{6x}{y}[/tex].
    Now I'm really lost as shouldn't the y be on the top or am I missing something realy stupid here?

    (ii) Similar problem to above - should get it from (i) but a hint would go a long way.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 3, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    The usual trick in the homogeneous case it to use the substitution y=u/x. Did you try that? It should make it separable.
     
  4. Dec 4, 2009 #3
    Many thanks, using a more appropriate substitution helps a lot. The second equation then just fell into place for me as a result.
     
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